topology.continuous_function.bounded ⟷ Mathlib.Topology.ContinuousFunction.Bounded

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Mario Carneiro, Yury Kudryashov, Heather Macbeth
 -/
 import Analysis.Normed.Order.Lattice
-import Analysis.NormedSpace.OperatorNorm
+import Analysis.NormedSpace.OperatorNorm.Basic
 import Analysis.NormedSpace.Star.Basic
 import Data.Real.Sqrt
 import Topology.ContinuousFunction.Algebra
@@ -652,7 +652,7 @@ variable [TopologicalSpace α] [CompactSpace α] [PseudoMetricSpace β]
 
 variable {f g : α →ᵇ β} {x : α} {C : ℝ}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (y z «expr ∈ » U) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (y z «expr ∈ » U) -/
 #print BoundedContinuousFunction.arzela_ascoli₁ /-
 /- Arzela-Ascoli theorem asserts that, on a compact space, a set of functions sharing
 a common modulus of continuity and taking values in a compact set forms a compact
@@ -874,16 +874,16 @@ theorem add_compContinuous [TopologicalSpace γ] (h : C(γ, α)) :
 @[simp]
 theorem coe_nsmulRec : ∀ n, ⇑(nsmulRec n f) = n • f
   | 0 => by rw [nsmulRec, zero_smul, coe_zero]
-  | n + 1 => by rw [nsmulRec, succ_nsmul, coe_add, coe_nsmul_rec]
+  | n + 1 => by rw [nsmulRec, succ_nsmul', coe_add, coe_nsmul_rec]
 #align bounded_continuous_function.coe_nsmul_rec BoundedContinuousFunction.coe_nsmulRec
 -/
 
-#print BoundedContinuousFunction.hasNatScalar /-
-instance hasNatScalar : SMul ℕ (α →ᵇ β)
+#print BoundedContinuousFunction.instSMulNat /-
+instance instSMulNat : SMul ℕ (α →ᵇ β)
     where smul n f :=
     { toContinuousMap := n • f.toContinuousMap
       map_bounded' := by simpa [coe_nsmul_rec] using (nsmulRec n f).map_bounded' }
-#align bounded_continuous_function.has_nat_scalar BoundedContinuousFunction.hasNatScalar
+#align bounded_continuous_function.has_nat_scalar BoundedContinuousFunction.instSMulNat
 -/
 
 #print BoundedContinuousFunction.coe_nsmul /-
@@ -1233,17 +1233,17 @@ theorem mkOfCompact_sub [CompactSpace α] (f g : C(α, β)) :
 #print BoundedContinuousFunction.coe_zsmulRec /-
 @[simp]
 theorem coe_zsmulRec : ∀ z, ⇑(zsmulRec z f) = z • f
-  | Int.ofNat n => by rw [zsmulRec, Int.ofNat_eq_coe, coe_nsmul_rec, coe_nat_zsmul]
+  | Int.ofNat n => by rw [zsmulRec, Int.ofNat_eq_coe, coe_nsmul_rec, natCast_zsmul]
   | -[n+1] => by rw [zsmulRec, negSucc_zsmul, coe_neg, coe_nsmul_rec]
 #align bounded_continuous_function.coe_zsmul_rec BoundedContinuousFunction.coe_zsmulRec
 -/
 
-#print BoundedContinuousFunction.hasIntScalar /-
-instance hasIntScalar : SMul ℤ (α →ᵇ β)
+#print BoundedContinuousFunction.instSMulInt /-
+instance instSMulInt : SMul ℤ (α →ᵇ β)
     where smul n f :=
     { toContinuousMap := n • f.toContinuousMap
       map_bounded' := by simpa using (zsmulRec n f).map_bounded' }
-#align bounded_continuous_function.has_int_scalar BoundedContinuousFunction.hasIntScalar
+#align bounded_continuous_function.has_int_scalar BoundedContinuousFunction.instSMulInt
 -/
 
 #print BoundedContinuousFunction.coe_zsmul /-
@@ -1586,7 +1586,7 @@ variable [SeminormedRing R]
 @[simp]
 theorem coe_npowRec (f : α →ᵇ R) : ∀ n, ⇑(npowRec n f) = f ^ n
   | 0 => by rw [npowRec, pow_zero, coe_one]
-  | n + 1 => by rw [npowRec, pow_succ, coe_mul, coe_npow_rec]
+  | n + 1 => by rw [npowRec, pow_succ', coe_mul, coe_npow_rec]
 #align bounded_continuous_function.coe_npow_rec BoundedContinuousFunction.coe_npowRec
 -/
 
@@ -1724,26 +1724,26 @@ functions from `α` to `β` is naturally a module over the algebra of bounded co
 functions from `α` to `𝕜`. -/
 
 
-#print BoundedContinuousFunction.hasSMul' /-
-instance hasSMul' : SMul (α →ᵇ 𝕜) (α →ᵇ β) :=
+#print BoundedContinuousFunction.instSMul' /-
+instance instSMul' : SMul (α →ᵇ 𝕜) (α →ᵇ β) :=
   ⟨fun (f : α →ᵇ 𝕜) (g : α →ᵇ β) =>
     ofNormedAddCommGroup (fun x => f x • g x) (f.Continuous.smul g.Continuous) (‖f‖ * ‖g‖) fun x =>
       calc
         ‖f x • g x‖ ≤ ‖f x‖ * ‖g x‖ := norm_smul_le _ _
         _ ≤ ‖f‖ * ‖g‖ :=
           mul_le_mul (f.norm_coe_le_norm _) (g.norm_coe_le_norm _) (norm_nonneg _) (norm_nonneg _)⟩
-#align bounded_continuous_function.has_smul' BoundedContinuousFunction.hasSMul'
+#align bounded_continuous_function.has_smul' BoundedContinuousFunction.instSMul'
 -/
 
-#print BoundedContinuousFunction.module' /-
-instance module' : Module (α →ᵇ 𝕜) (α →ᵇ β) :=
+#print BoundedContinuousFunction.instModule' /-
+instance instModule' : Module (α →ᵇ 𝕜) (α →ᵇ β) :=
   Module.ofMinimalAxioms <|
     { smul := (· • ·)
       smul_add := fun c f₁ f₂ => ext fun x => smul_add _ _ _
       add_smul := fun c₁ c₂ f => ext fun x => add_smul _ _ _
       hMul_smul := fun c₁ c₂ f => ext fun x => hMul_smul _ _ _
       one_smul := fun f => ext fun x => one_smul 𝕜 (f x) }
-#align bounded_continuous_function.module' BoundedContinuousFunction.module'
+#align bounded_continuous_function.module' BoundedContinuousFunction.instModule'
 -/
 
 /- warning: bounded_continuous_function.norm_smul_le clashes with norm_smul_le -> norm_smul_le
@@ -1901,18 +1901,18 @@ instance : SemilatticeSup (α →ᵇ β) :=
 instance : Lattice (α →ᵇ β) :=
   { BoundedContinuousFunction.semilatticeSup, BoundedContinuousFunction.semilatticeInf with }
 
-#print BoundedContinuousFunction.coeFn_sup /-
+#print BoundedContinuousFunction.coe_sup /-
 @[simp]
-theorem coeFn_sup (f g : α →ᵇ β) : ⇑(f ⊔ g) = f ⊔ g :=
+theorem coe_sup (f g : α →ᵇ β) : ⇑(f ⊔ g) = f ⊔ g :=
   rfl
-#align bounded_continuous_function.coe_fn_sup BoundedContinuousFunction.coeFn_sup
+#align bounded_continuous_function.coe_fn_sup BoundedContinuousFunction.coe_sup
 -/
 
-#print BoundedContinuousFunction.coeFn_abs /-
+#print BoundedContinuousFunction.coe_abs /-
 @[simp]
-theorem coeFn_abs (f : α →ᵇ β) : ⇑|f| = |f| :=
+theorem coe_abs (f : α →ᵇ β) : ⇑|f| = |f| :=
   rfl
-#align bounded_continuous_function.coe_fn_abs BoundedContinuousFunction.coeFn_abs
+#align bounded_continuous_function.coe_fn_abs BoundedContinuousFunction.coe_abs
 -/
 
 instance : NormedLatticeAddCommGroup (α →ᵇ β) :=

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

@@ -662,7 +662,7 @@ and several useful variations around it. -/
 theorem arzela_ascoli₁ [CompactSpace β] (A : Set (α →ᵇ β)) (closed : IsClosed A)
     (H : Equicontinuous (coeFn : A → α → β)) : IsCompact A :=
   by
-  simp_rw [Equicontinuous, Metric.equicontinuousAt_iff_pair] at H 
+  simp_rw [Equicontinuous, Metric.equicontinuousAt_iff_pair] at H
   refine' isCompact_of_totallyBounded_isClosed _ closed
   refine' totally_bounded_of_finite_discretization fun ε ε0 => _
   rcases exists_between ε0 with ⟨ε₁, ε₁0, εε₁⟩
@@ -1764,8 +1764,8 @@ theorem NNReal.upper_bound {α : Type _} [TopologicalSpace α] (f : α →ᵇ 
     f x ≤ nndist f 0 :=
   by
   have key : nndist (f x) ((0 : α →ᵇ ℝ≥0) x) ≤ nndist f 0 := @dist_coe_le_dist α ℝ≥0 _ _ f 0 x
-  simp only [coe_zero, Pi.zero_apply] at key 
-  rwa [NNReal.nndist_zero_eq_val' (f x)] at key 
+  simp only [coe_zero, Pi.zero_apply] at key
+  rwa [NNReal.nndist_zero_eq_val' (f x)] at key
 #align bounded_continuous_function.nnreal.upper_bound BoundedContinuousFunction.NNReal.upper_bound
 -/
 

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

@@ -1507,7 +1507,7 @@ protected def ContinuousLinearMap.compLeftContinuousBounded (g : β →L[𝕜] 
   LinearMap.mkContinuous
     { toFun := fun f =>
         ofNormedAddCommGroup (g ∘ f) (g.Continuous.comp f.Continuous) (‖g‖ * ‖f‖) fun x =>
-          g.le_op_norm_of_le (f.norm_coe_le_norm x)
+          g.le_opNorm_of_le (f.norm_coe_le_norm x)
       map_add' := fun f g => by ext <;> simp
       map_smul' := fun c f => by ext <;> simp } ‖g‖ fun f =>
     norm_ofNormedAddCommGroup_le _ (mul_nonneg (norm_nonneg g) (norm_nonneg f)) _

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

@@ -1432,20 +1432,20 @@ instance : Module 𝕜 (α →ᵇ β) :=
 
 variable (𝕜)
 
-#print BoundedContinuousFunction.evalClm /-
+#print BoundedContinuousFunction.evalCLM /-
 /-- The evaluation at a point, as a continuous linear map from `α →ᵇ β` to `β`. -/
-def evalClm (x : α) : (α →ᵇ β) →L[𝕜] β where
+def evalCLM (x : α) : (α →ᵇ β) →L[𝕜] β where
   toFun f := f x
   map_add' f g := add_apply _ _
   map_smul' c f := smul_apply _ _ _
-#align bounded_continuous_function.eval_clm BoundedContinuousFunction.evalClm
+#align bounded_continuous_function.eval_clm BoundedContinuousFunction.evalCLM
 -/
 
-#print BoundedContinuousFunction.evalClm_apply /-
+#print BoundedContinuousFunction.evalCLM_apply /-
 @[simp]
-theorem evalClm_apply (x : α) (f : α →ᵇ β) : evalClm 𝕜 x f = f x :=
+theorem evalCLM_apply (x : α) (f : α →ᵇ β) : evalCLM 𝕜 x f = f x :=
   rfl
-#align bounded_continuous_function.eval_clm_apply BoundedContinuousFunction.evalClm_apply
+#align bounded_continuous_function.eval_clm_apply BoundedContinuousFunction.evalCLM_apply
 -/
 
 variable (α β)

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

@@ -84,7 +84,7 @@ instance : BoundedContinuousMapClass (α →ᵇ β) α β
 /-- Helper instance for when there's too many metavariables to apply `fun_like.has_coe_to_fun`
 directly. -/
 instance : CoeFun (α →ᵇ β) fun _ => α → β :=
-  FunLike.hasCoeToFun
+  DFunLike.hasCoeToFun
 
 instance [BoundedContinuousMapClass F α β] : CoeTC F (α →ᵇ β) :=
   ⟨fun f =>
@@ -124,7 +124,7 @@ protected theorem continuous (f : α →ᵇ β) : Continuous f :=
 #print BoundedContinuousFunction.ext /-
 @[ext]
 theorem ext (h : ∀ x, f x = g x) : f = g :=
-  FunLike.ext _ _ h
+  DFunLike.ext _ _ h
 #align bounded_continuous_function.ext BoundedContinuousFunction.ext
 -/
 
@@ -605,7 +605,7 @@ theorem extend_apply' {f : α ↪ δ} {x : δ} (hx : x ∉ range f) (g : α →
 
 #print BoundedContinuousFunction.extend_of_empty /-
 theorem extend_of_empty [IsEmpty α] (f : α ↪ δ) (g : α →ᵇ β) (h : δ →ᵇ β) : extend f g h = h :=
-  FunLike.coe_injective <| Function.extend_of_isEmpty f g h
+  DFunLike.coe_injective <| Function.extend_of_isEmpty f g h
 #align bounded_continuous_function.extend_of_empty BoundedContinuousFunction.extend_of_empty
 -/
 
@@ -794,7 +794,7 @@ theorem mkOfCompact_one [CompactSpace α] : mkOfCompact (1 : C(α, β)) = 1 :=
 #print BoundedContinuousFunction.forall_coe_one_iff_one /-
 @[to_additive]
 theorem forall_coe_one_iff_one (f : α →ᵇ β) : (∀ x, f x = 1) ↔ f = 1 :=
-  (@FunLike.ext_iff _ _ _ _ f 1).symm
+  (@DFunLike.ext_iff _ _ _ _ f 1).symm
 #align bounded_continuous_function.forall_coe_one_iff_one BoundedContinuousFunction.forall_coe_one_iff_one
 #align bounded_continuous_function.forall_coe_zero_iff_zero BoundedContinuousFunction.forall_coe_zero_iff_zero
 -/
@@ -901,7 +901,7 @@ theorem nsmul_apply (r : ℕ) (f : α →ᵇ β) (v : α) : (r • f) v = r •
 -/
 
 instance : AddMonoid (α →ᵇ β) :=
-  FunLike.coe_injective.AddMonoid _ coe_zero coe_add fun _ _ => coe_nsmul _ _
+  DFunLike.coe_injective.AddMonoid _ coe_zero coe_add fun _ _ => coe_nsmul _ _
 
 instance : LipschitzAdd (α →ᵇ β)
     where lipschitz_add :=
@@ -1261,7 +1261,7 @@ theorem zsmul_apply (r : ℤ) (f : α →ᵇ β) (v : α) : (r • f) v = r •
 -/
 
 instance : AddCommGroup (α →ᵇ β) :=
-  FunLike.coe_injective.AddCommGroup _ coe_zero coe_add coe_neg coe_sub (fun _ _ => coe_nsmul _ _)
+  DFunLike.coe_injective.AddCommGroup _ coe_zero coe_add coe_neg coe_sub (fun _ _ => coe_nsmul _ _)
     fun _ _ => coe_zsmul _ _
 
 instance : SeminormedAddCommGroup (α →ᵇ β)
@@ -1404,7 +1404,7 @@ section MulAction
 variable [MonoidWithZero 𝕜] [Zero β] [MulAction 𝕜 β] [BoundedSMul 𝕜 β]
 
 instance : MulAction 𝕜 (α →ᵇ β) :=
-  FunLike.coe_injective.MulAction _ coe_smul
+  DFunLike.coe_injective.MulAction _ coe_smul
 
 end MulAction
 
@@ -1415,7 +1415,7 @@ variable [MonoidWithZero 𝕜] [AddMonoid β] [DistribMulAction 𝕜 β] [Bounde
 variable [LipschitzAdd β]
 
 instance : DistribMulAction 𝕜 (α →ᵇ β) :=
-  Function.Injective.distribMulAction ⟨_, coe_zero, coe_add⟩ FunLike.coe_injective coe_smul
+  Function.Injective.distribMulAction ⟨_, coe_zero, coe_add⟩ DFunLike.coe_injective coe_smul
 
 end DistribMulAction
 
@@ -1428,7 +1428,7 @@ variable {f g : α →ᵇ β} {x : α} {C : ℝ}
 variable [LipschitzAdd β]
 
 instance : Module 𝕜 (α →ᵇ β) :=
-  Function.Injective.module _ ⟨_, coe_zero, coe_add⟩ FunLike.coe_injective coe_smul
+  Function.Injective.module _ ⟨_, coe_zero, coe_add⟩ DFunLike.coe_injective coe_smul
 
 variable (𝕜)
 
@@ -1562,7 +1562,7 @@ theorem mul_apply (f g : α →ᵇ R) (x : α) : (f * g) x = f x * g x :=
 -/
 
 instance : NonUnitalRing (α →ᵇ R) :=
-  FunLike.coe_injective.NonUnitalRing _ coe_zero coe_add coe_mul coe_neg coe_sub
+  DFunLike.coe_injective.NonUnitalRing _ coe_zero coe_add coe_mul coe_neg coe_sub
     (fun _ _ => coe_nsmul _ _) fun _ _ => coe_zsmul _ _
 
 instance : NonUnitalSeminormedRing (α →ᵇ R) :=
@@ -1633,7 +1633,7 @@ theorem coe_intCast (n : ℤ) : ((n : α →ᵇ R) : α → R) = n :=
 -/
 
 instance : Ring (α →ᵇ R) :=
-  FunLike.coe_injective.Ring _ coe_zero coe_one coe_add coe_mul coe_neg coe_sub
+  DFunLike.coe_injective.Ring _ coe_zero coe_one coe_add coe_mul coe_neg coe_sub
     (fun _ _ => coe_nsmul _ _) (fun _ _ => coe_zsmul _ _) (fun _ _ => coe_pow _ _) coe_natCast
     coe_intCast
 

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

@@ -1939,7 +1939,7 @@ variable [TopologicalSpace α]
 /-- The nonnegative part of a bounded continuous `ℝ`-valued function as a bounded
 continuous `ℝ≥0`-valued function. -/
 def nnrealPart (f : α →ᵇ ℝ) : α →ᵇ ℝ≥0 :=
-  BoundedContinuousFunction.comp _ (show LipschitzWith 1 Real.toNNReal from lipschitzWith_pos) f
+  BoundedContinuousFunction.comp _ (show LipschitzWith 1 Real.toNNReal from lipschitzWith_posPart) f
 #align bounded_continuous_function.nnreal_part BoundedContinuousFunction.nnrealPart
 -/
 

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

@@ -1724,15 +1724,15 @@ functions from `α` to `β` is naturally a module over the algebra of bounded co
 functions from `α` to `𝕜`. -/
 
 
-#print BoundedContinuousFunction.hasSmul' /-
-instance hasSmul' : SMul (α →ᵇ 𝕜) (α →ᵇ β) :=
+#print BoundedContinuousFunction.hasSMul' /-
+instance hasSMul' : SMul (α →ᵇ 𝕜) (α →ᵇ β) :=
   ⟨fun (f : α →ᵇ 𝕜) (g : α →ᵇ β) =>
     ofNormedAddCommGroup (fun x => f x • g x) (f.Continuous.smul g.Continuous) (‖f‖ * ‖g‖) fun x =>
       calc
         ‖f x • g x‖ ≤ ‖f x‖ * ‖g x‖ := norm_smul_le _ _
         _ ≤ ‖f‖ * ‖g‖ :=
           mul_le_mul (f.norm_coe_le_norm _) (g.norm_coe_le_norm _) (norm_nonneg _) (norm_nonneg _)⟩
-#align bounded_continuous_function.has_smul' BoundedContinuousFunction.hasSmul'
+#align bounded_continuous_function.has_smul' BoundedContinuousFunction.hasSMul'
 -/
 
 #print BoundedContinuousFunction.module' /-

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

@@ -1737,7 +1737,7 @@ instance hasSmul' : SMul (α →ᵇ 𝕜) (α →ᵇ β) :=
 
 #print BoundedContinuousFunction.module' /-
 instance module' : Module (α →ᵇ 𝕜) (α →ᵇ β) :=
-  Module.ofCore <|
+  Module.ofMinimalAxioms <|
     { smul := (· • ·)
       smul_add := fun c f₁ f₂ => ext fun x => smul_add _ _ _
       add_smul := fun c₁ c₂ f => ext fun x => add_smul _ _ _

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

@@ -1746,10 +1746,12 @@ instance module' : Module (α →ᵇ 𝕜) (α →ᵇ β) :=
 #align bounded_continuous_function.module' BoundedContinuousFunction.module'
 -/
 
-#print BoundedContinuousFunction.norm_smul_le /-
+/- warning: bounded_continuous_function.norm_smul_le clashes with norm_smul_le -> norm_smul_le
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.norm_smul_le norm_smul_leₓ'. -/
+#print norm_smul_le /-
 theorem norm_smul_le (f : α →ᵇ 𝕜) (g : α →ᵇ β) : ‖f • g‖ ≤ ‖f‖ * ‖g‖ :=
   norm_ofNormedAddCommGroup_le _ (mul_nonneg (norm_nonneg _) (norm_nonneg _)) _
-#align bounded_continuous_function.norm_smul_le BoundedContinuousFunction.norm_smul_le
+#align bounded_continuous_function.norm_smul_le norm_smul_le
 -/
 
 /- TODO: When `normed_module` has been added to `normed_space.basic`, the above facts

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

@@ -1757,14 +1757,14 @@ show that the space of bounded continuous functions from `α` to `β` is natural
 module over the algebra of bounded continuous functions from `α` to `𝕜`. -/
 end NormedAlgebra
 
-#print BoundedContinuousFunction.Nnreal.upper_bound /-
-theorem Nnreal.upper_bound {α : Type _} [TopologicalSpace α] (f : α →ᵇ ℝ≥0) (x : α) :
+#print BoundedContinuousFunction.NNReal.upper_bound /-
+theorem NNReal.upper_bound {α : Type _} [TopologicalSpace α] (f : α →ᵇ ℝ≥0) (x : α) :
     f x ≤ nndist f 0 :=
   by
   have key : nndist (f x) ((0 : α →ᵇ ℝ≥0) x) ≤ nndist f 0 := @dist_coe_le_dist α ℝ≥0 _ _ f 0 x
   simp only [coe_zero, Pi.zero_apply] at key 
   rwa [NNReal.nndist_zero_eq_val' (f x)] at key 
-#align bounded_continuous_function.nnreal.upper_bound BoundedContinuousFunction.Nnreal.upper_bound
+#align bounded_continuous_function.nnreal.upper_bound BoundedContinuousFunction.NNReal.upper_bound
 -/
 
 /-!

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

@@ -3,12 +3,12 @@ Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Mario Carneiro, Yury Kudryashov, Heather Macbeth
 -/
-import Mathbin.Analysis.Normed.Order.Lattice
-import Mathbin.Analysis.NormedSpace.OperatorNorm
-import Mathbin.Analysis.NormedSpace.Star.Basic
-import Mathbin.Data.Real.Sqrt
-import Mathbin.Topology.ContinuousFunction.Algebra
-import Mathbin.Topology.MetricSpace.Equicontinuity
+import Analysis.Normed.Order.Lattice
+import Analysis.NormedSpace.OperatorNorm
+import Analysis.NormedSpace.Star.Basic
+import Data.Real.Sqrt
+import Topology.ContinuousFunction.Algebra
+import Topology.MetricSpace.Equicontinuity
 
 #align_import topology.continuous_function.bounded from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"
 
@@ -652,7 +652,7 @@ variable [TopologicalSpace α] [CompactSpace α] [PseudoMetricSpace β]
 
 variable {f g : α →ᵇ β} {x : α} {C : ℝ}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y z «expr ∈ » U) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (y z «expr ∈ » U) -/
 #print BoundedContinuousFunction.arzela_ascoli₁ /-
 /- Arzela-Ascoli theorem asserts that, on a compact space, a set of functions sharing
 a common modulus of continuity and taking values in a compact set forms a compact
@@ -735,7 +735,7 @@ theorem arzela_ascoli₂ (s : Set β) (hs : IsCompact s) (A : Set (α →ᵇ β)
   have M : LipschitzWith 1 coe := LipschitzWith.subtype_val s
   let F : (α →ᵇ s) → α →ᵇ β := comp coe M
   refine'
-    isCompact_of_isClosed_subset ((_ : IsCompact (F ⁻¹' A)).image (continuous_comp M)) closed
+    IsCompact.of_isClosed_subset ((_ : IsCompact (F ⁻¹' A)).image (continuous_comp M)) closed
       fun f hf => _
   · haveI : CompactSpace s := isCompact_iff_compactSpace.1 hs
     refine' arzela_ascoli₁ _ (continuous_iff_isClosed.1 (continuous_comp M) _ closed) _

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

@@ -128,16 +128,16 @@ theorem ext (h : ∀ x, f x = g x) : f = g :=
 #align bounded_continuous_function.ext BoundedContinuousFunction.ext
 -/
 
-#print BoundedContinuousFunction.bounded_range /-
-theorem bounded_range (f : α →ᵇ β) : Bounded (range f) :=
-  bounded_range_iff.2 f.Bounded
-#align bounded_continuous_function.bounded_range BoundedContinuousFunction.bounded_range
+#print BoundedContinuousFunction.isBounded_range /-
+theorem isBounded_range (f : α →ᵇ β) : IsBounded (range f) :=
+  isBounded_range_iff.2 f.Bounded
+#align bounded_continuous_function.bounded_range BoundedContinuousFunction.isBounded_range
 -/
 
-#print BoundedContinuousFunction.bounded_image /-
-theorem bounded_image (f : α →ᵇ β) (s : Set α) : Bounded (f '' s) :=
-  f.bounded_range.mono <| image_subset_range _ _
-#align bounded_continuous_function.bounded_image BoundedContinuousFunction.bounded_image
+#print BoundedContinuousFunction.isBounded_image /-
+theorem isBounded_image (f : α →ᵇ β) (s : Set α) : IsBounded (f '' s) :=
+  f.isBounded_range.mono <| image_subset_range _ _
+#align bounded_continuous_function.bounded_image BoundedContinuousFunction.isBounded_image
 -/
 
 #print BoundedContinuousFunction.eq_of_empty /-
@@ -163,7 +163,7 @@ theorem mkOfBound_coe {f} {C} {h} : (mkOfBound f C h : α → β) = (f : α →
 #print BoundedContinuousFunction.mkOfCompact /-
 /-- A continuous function on a compact space is automatically a bounded continuous function. -/
 def mkOfCompact [CompactSpace α] (f : C(α, β)) : α →ᵇ β :=
-  ⟨f, bounded_range_iff.1 (isCompact_range f.Continuous).Bounded⟩
+  ⟨f, isBounded_range_iff.1 (isCompact_range f.Continuous).Bounded⟩
 #align bounded_continuous_function.mk_of_compact BoundedContinuousFunction.mkOfCompact
 -/
 
@@ -577,7 +577,7 @@ def extend (f : α ↪ δ) (g : α →ᵇ β) (h : δ →ᵇ β) : δ →ᵇ β
   continuous_toFun := continuous_of_discreteTopology
   map_bounded' :=
     by
-    rw [← bounded_range_iff, range_extend f.injective, Metric.bounded_union]
+    rw [← bounded_range_iff, range_extend f.injective, Bornology.isBounded_union]
     exact ⟨g.bounded_range, h.bounded_image _⟩
 #align bounded_continuous_function.extend BoundedContinuousFunction.extend
 -/
@@ -1158,7 +1158,7 @@ theorem norm_normComp : ‖f.normComp‖ = ‖f‖ := by simp only [norm_eq, coe
 
 #print BoundedContinuousFunction.bddAbove_range_norm_comp /-
 theorem bddAbove_range_norm_comp : BddAbove <| Set.range <| norm ∘ f :=
-  (Real.bounded_iff_bddBelow_bddAbove.mp <| @bounded_range _ _ _ _ f.normComp).2
+  (Real.isBounded_iff_bddBelow_bddAbove.mp <| @isBounded_range _ _ _ _ f.normComp).2
 #align bounded_continuous_function.bdd_above_range_norm_comp BoundedContinuousFunction.bddAbove_range_norm_comp
 -/
 

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

@@ -1567,7 +1567,7 @@ instance : NonUnitalRing (α →ᵇ R) :=
 
 instance : NonUnitalSeminormedRing (α →ᵇ R) :=
   { BoundedContinuousFunction.seminormedAddCommGroup with
-    norm_mul := fun f g =>
+    norm_hMul := fun f g =>
       norm_ofNormedAddCommGroup_le _ (mul_nonneg (norm_nonneg _) (norm_nonneg _)) _ }
 
 end SemiNormed
@@ -1693,7 +1693,7 @@ variable {f g : α →ᵇ γ} {x : α} {c : 𝕜}
 def C : 𝕜 →+* α →ᵇ γ where
   toFun := fun c : 𝕜 => const α ((algebraMap 𝕜 γ) c)
   map_one' := ext fun x => (algebraMap 𝕜 γ).map_one
-  map_mul' c₁ c₂ := ext fun x => (algebraMap 𝕜 γ).map_mul _ _
+  map_mul' c₁ c₂ := ext fun x => (algebraMap 𝕜 γ).map_hMul _ _
   map_zero' := ext fun x => (algebraMap 𝕜 γ).map_zero
   map_add' c₁ c₂ := ext fun x => (algebraMap 𝕜 γ).map_add _ _
 #align bounded_continuous_function.C BoundedContinuousFunction.C
@@ -1741,7 +1741,7 @@ instance module' : Module (α →ᵇ 𝕜) (α →ᵇ β) :=
     { smul := (· • ·)
       smul_add := fun c f₁ f₂ => ext fun x => smul_add _ _ _
       add_smul := fun c₁ c₂ f => ext fun x => add_smul _ _ _
-      mul_smul := fun c₁ c₂ f => ext fun x => mul_smul _ _ _
+      hMul_smul := fun c₁ c₂ f => ext fun x => hMul_smul _ _ _
       one_smul := fun f => ext fun x => one_smul 𝕜 (f x) }
 #align bounded_continuous_function.module' BoundedContinuousFunction.module'
 -/
@@ -1829,24 +1829,24 @@ variable [NonUnitalNormedRing β] [StarRing β]
 
 instance [NormedStarGroup β] : StarRing (α →ᵇ β) :=
   { BoundedContinuousFunction.starAddMonoid with
-    star_mul := fun f g => ext fun x => star_mul (f x) (g x) }
+    star_hMul := fun f g => ext fun x => star_hMul (f x) (g x) }
 
 variable [CstarRing β]
 
 instance : CstarRing (α →ᵇ β)
-    where norm_star_mul_self := by
+    where norm_star_hMul_self := by
     intro f
     refine' le_antisymm _ _
     · rw [← sq, norm_le (sq_nonneg _)]
       dsimp [star_apply]
       intro x
-      rw [CstarRing.norm_star_mul_self, ← sq]
+      rw [CstarRing.norm_star_hMul_self, ← sq]
       refine' sq_le_sq' _ _
       · linarith [norm_nonneg (f x), norm_nonneg f]
       · exact norm_coe_le_norm f x
     · rw [← sq, ← Real.le_sqrt (norm_nonneg _) (norm_nonneg _), norm_le (Real.sqrt_nonneg _)]
       intro x
-      rw [Real.le_sqrt (norm_nonneg _) (norm_nonneg _), sq, ← CstarRing.norm_star_mul_self]
+      rw [Real.le_sqrt (norm_nonneg _) (norm_nonneg _), sq, ← CstarRing.norm_star_hMul_self]
       exact norm_coe_le_norm (star f * f) x
 
 end CstarRing

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

@@ -2,11 +2,6 @@
 Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Mario Carneiro, Yury Kudryashov, Heather Macbeth
-
-! This file was ported from Lean 3 source module topology.continuous_function.bounded
-! leanprover-community/mathlib commit 4280f5f32e16755ec7985ce11e189b6cd6ff6735
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Normed.Order.Lattice
 import Mathbin.Analysis.NormedSpace.OperatorNorm
@@ -15,6 +10,8 @@ import Mathbin.Data.Real.Sqrt
 import Mathbin.Topology.ContinuousFunction.Algebra
 import Mathbin.Topology.MetricSpace.Equicontinuity
 
+#align_import topology.continuous_function.bounded from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"
+
 /-!
 # Bounded continuous functions
 
@@ -655,7 +652,7 @@ variable [TopologicalSpace α] [CompactSpace α] [PseudoMetricSpace β]
 
 variable {f g : α →ᵇ β} {x : α} {C : ℝ}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (y z «expr ∈ » U) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y z «expr ∈ » U) -/
 #print BoundedContinuousFunction.arzela_ascoli₁ /-
 /- Arzela-Ascoli theorem asserts that, on a compact space, a set of functions sharing
 a common modulus of continuity and taking values in a compact set forms a compact

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

@@ -1911,7 +1911,7 @@ theorem coeFn_sup (f g : α →ᵇ β) : ⇑(f ⊔ g) = f ⊔ g :=
 
 #print BoundedContinuousFunction.coeFn_abs /-
 @[simp]
-theorem coeFn_abs (f : α →ᵇ β) : ⇑(|f|) = |f| :=
+theorem coeFn_abs (f : α →ᵇ β) : ⇑|f| = |f| :=
   rfl
 #align bounded_continuous_function.coe_fn_abs BoundedContinuousFunction.coeFn_abs
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/d30d31261cdb4d2f5e612eabc3c4bf45556350d5

@@ -417,7 +417,7 @@ theorem continuous_eval_const {x : α} : Continuous fun f : α →ᵇ β => f x
 /-- The evaluation map is continuous, as a joint function of `u` and `x` -/
 @[continuity]
 theorem continuous_eval : Continuous fun p : (α →ᵇ β) × α => p.1 p.2 :=
-  (continuous_prod_of_continuous_lipschitz _ 1 fun f => f.Continuous) <| lipschitz_evalx
+  (continuous_prod_of_continuous_lipschitzWith _ 1 fun f => f.Continuous) <| lipschitz_evalx
 #align bounded_continuous_function.continuous_eval BoundedContinuousFunction.continuous_eval
 -/
 

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

@@ -51,7 +51,6 @@ structure BoundedContinuousFunction (α : Type u) (β : Type v) [TopologicalSpac
 #align bounded_continuous_function BoundedContinuousFunction
 -/
 
--- mathport name: bounded_continuous_function
 scoped[BoundedContinuousFunction] infixr:25 " →ᵇ " => BoundedContinuousFunction
 
 section
@@ -96,10 +95,12 @@ instance [BoundedContinuousMapClass F α β] : CoeTC F (α →ᵇ β) :=
       continuous_toFun := map_continuous f
       map_bounded' := map_bounded f }⟩
 
+#print BoundedContinuousFunction.coe_to_continuous_fun /-
 @[simp]
 theorem coe_to_continuous_fun (f : α →ᵇ β) : (f.toContinuousMap : α → β) = f :=
   rfl
 #align bounded_continuous_function.coe_to_continuous_fun BoundedContinuousFunction.coe_to_continuous_fun
+-/
 
 #print BoundedContinuousFunction.Simps.apply /-
 /-- See Note [custom simps projection]. We need to specify this projection explicitly in this case,
@@ -111,26 +112,36 @@ def Simps.apply (h : α →ᵇ β) : α → β :=
 
 initialize_simps_projections BoundedContinuousFunction (to_continuous_map_to_fun → apply)
 
+#print BoundedContinuousFunction.bounded /-
 protected theorem bounded (f : α →ᵇ β) : ∃ C, ∀ x y : α, dist (f x) (f y) ≤ C :=
   f.map_bounded'
 #align bounded_continuous_function.bounded BoundedContinuousFunction.bounded
+-/
 
+#print BoundedContinuousFunction.continuous /-
 protected theorem continuous (f : α →ᵇ β) : Continuous f :=
   f.toContinuousMap.Continuous
 #align bounded_continuous_function.continuous BoundedContinuousFunction.continuous
+-/
 
+#print BoundedContinuousFunction.ext /-
 @[ext]
 theorem ext (h : ∀ x, f x = g x) : f = g :=
   FunLike.ext _ _ h
 #align bounded_continuous_function.ext BoundedContinuousFunction.ext
+-/
 
+#print BoundedContinuousFunction.bounded_range /-
 theorem bounded_range (f : α →ᵇ β) : Bounded (range f) :=
   bounded_range_iff.2 f.Bounded
 #align bounded_continuous_function.bounded_range BoundedContinuousFunction.bounded_range
+-/
 
+#print BoundedContinuousFunction.bounded_image /-
 theorem bounded_image (f : α →ᵇ β) (s : Set α) : Bounded (f '' s) :=
   f.bounded_range.mono <| image_subset_range _ _
 #align bounded_continuous_function.bounded_image BoundedContinuousFunction.bounded_image
+-/
 
 #print BoundedContinuousFunction.eq_of_empty /-
 theorem eq_of_empty [IsEmpty α] (f g : α →ᵇ β) : f = g :=
@@ -138,15 +149,19 @@ theorem eq_of_empty [IsEmpty α] (f g : α →ᵇ β) : f = g :=
 #align bounded_continuous_function.eq_of_empty BoundedContinuousFunction.eq_of_empty
 -/
 
+#print BoundedContinuousFunction.mkOfBound /-
 /-- A continuous function with an explicit bound is a bounded continuous function. -/
 def mkOfBound (f : C(α, β)) (C : ℝ) (h : ∀ x y : α, dist (f x) (f y) ≤ C) : α →ᵇ β :=
   ⟨f, ⟨C, h⟩⟩
 #align bounded_continuous_function.mk_of_bound BoundedContinuousFunction.mkOfBound
+-/
 
+#print BoundedContinuousFunction.mkOfBound_coe /-
 @[simp]
 theorem mkOfBound_coe {f} {C} {h} : (mkOfBound f C h : α → β) = (f : α → β) :=
   rfl
 #align bounded_continuous_function.mk_of_bound_coe BoundedContinuousFunction.mkOfBound_coe
+-/
 
 #print BoundedContinuousFunction.mkOfCompact /-
 /-- A continuous function on a compact space is automatically a bounded continuous function. -/
@@ -155,11 +170,14 @@ def mkOfCompact [CompactSpace α] (f : C(α, β)) : α →ᵇ β :=
 #align bounded_continuous_function.mk_of_compact BoundedContinuousFunction.mkOfCompact
 -/
 
+#print BoundedContinuousFunction.mkOfCompact_apply /-
 @[simp]
 theorem mkOfCompact_apply [CompactSpace α] (f : C(α, β)) (a : α) : mkOfCompact f a = f a :=
   rfl
 #align bounded_continuous_function.mk_of_compact_apply BoundedContinuousFunction.mkOfCompact_apply
+-/
 
+#print BoundedContinuousFunction.mkOfDiscrete /-
 /-- If a function is bounded on a discrete space, it is automatically continuous,
 and therefore gives rise to an element of the type of bounded continuous functions -/
 @[simps]
@@ -167,15 +185,19 @@ def mkOfDiscrete [DiscreteTopology α] (f : α → β) (C : ℝ) (h : ∀ x y :
     α →ᵇ β :=
   ⟨⟨f, continuous_of_discreteTopology⟩, ⟨C, h⟩⟩
 #align bounded_continuous_function.mk_of_discrete BoundedContinuousFunction.mkOfDiscrete
+-/
 
 /-- The uniform distance between two bounded continuous functions -/
 instance : Dist (α →ᵇ β) :=
   ⟨fun f g => sInf {C | 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C}⟩
 
+#print BoundedContinuousFunction.dist_eq /-
 theorem dist_eq : dist f g = sInf {C | 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C} :=
   rfl
 #align bounded_continuous_function.dist_eq BoundedContinuousFunction.dist_eq
+-/
 
+#print BoundedContinuousFunction.dist_set_exists /-
 theorem dist_set_exists : ∃ C, 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C :=
   by
   rcases f.bounded_range.union g.bounded_range with ⟨C, hC⟩
@@ -183,11 +205,14 @@ theorem dist_set_exists : ∃ C, 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C
       right] <;>
     apply mem_range_self
 #align bounded_continuous_function.dist_set_exists BoundedContinuousFunction.dist_set_exists
+-/
 
+#print BoundedContinuousFunction.dist_coe_le_dist /-
 /-- The pointwise distance is controlled by the distance between functions, by definition. -/
 theorem dist_coe_le_dist (x : α) : dist (f x) (g x) ≤ dist f g :=
   le_csInf dist_set_exists fun b hb => hb.2 x
 #align bounded_continuous_function.dist_coe_le_dist BoundedContinuousFunction.dist_coe_le_dist
+-/
 
 /- This lemma will be needed in the proof of the metric space instance, but it will become
 useless afterwards as it will be superseded by the general result that the distance is nonnegative
@@ -195,16 +220,21 @@ in metric spaces. -/
 private theorem dist_nonneg' : 0 ≤ dist f g :=
   le_csInf dist_set_exists fun C => And.left
 
+#print BoundedContinuousFunction.dist_le /-
 /-- The distance between two functions is controlled by the supremum of the pointwise distances -/
 theorem dist_le (C0 : (0 : ℝ) ≤ C) : dist f g ≤ C ↔ ∀ x : α, dist (f x) (g x) ≤ C :=
   ⟨fun h x => le_trans (dist_coe_le_dist x) h, fun H => csInf_le ⟨0, fun C => And.left⟩ ⟨C0, H⟩⟩
 #align bounded_continuous_function.dist_le BoundedContinuousFunction.dist_le
+-/
 
+#print BoundedContinuousFunction.dist_le_iff_of_nonempty /-
 theorem dist_le_iff_of_nonempty [Nonempty α] : dist f g ≤ C ↔ ∀ x, dist (f x) (g x) ≤ C :=
   ⟨fun h x => le_trans (dist_coe_le_dist x) h, fun w =>
     (dist_le (le_trans dist_nonneg (w (Nonempty.some ‹_›)))).mpr w⟩
 #align bounded_continuous_function.dist_le_iff_of_nonempty BoundedContinuousFunction.dist_le_iff_of_nonempty
+-/
 
+#print BoundedContinuousFunction.dist_lt_of_nonempty_compact /-
 theorem dist_lt_of_nonempty_compact [Nonempty α] [CompactSpace α]
     (w : ∀ x : α, dist (f x) (g x) < C) : dist f g < C :=
   by
@@ -213,7 +243,9 @@ theorem dist_lt_of_nonempty_compact [Nonempty α] [CompactSpace α]
     IsCompact.exists_forall_ge isCompact_univ Set.univ_nonempty (Continuous.continuousOn c)
   exact lt_of_le_of_lt (dist_le_iff_of_nonempty.mpr fun y => le y trivial) (w x)
 #align bounded_continuous_function.dist_lt_of_nonempty_compact BoundedContinuousFunction.dist_lt_of_nonempty_compact
+-/
 
+#print BoundedContinuousFunction.dist_lt_iff_of_compact /-
 theorem dist_lt_iff_of_compact [CompactSpace α] (C0 : (0 : ℝ) < C) :
     dist f g < C ↔ ∀ x : α, dist (f x) (g x) < C :=
   by
@@ -229,11 +261,14 @@ theorem dist_lt_iff_of_compact [CompactSpace α] (C0 : (0 : ℝ) < C) :
       rw [dist_eq]
       exact csInf_le ⟨0, fun C => And.left⟩ ⟨le_rfl, fun x => False.elim (h (Nonempty.intro x))⟩
 #align bounded_continuous_function.dist_lt_iff_of_compact BoundedContinuousFunction.dist_lt_iff_of_compact
+-/
 
+#print BoundedContinuousFunction.dist_lt_iff_of_nonempty_compact /-
 theorem dist_lt_iff_of_nonempty_compact [Nonempty α] [CompactSpace α] :
     dist f g < C ↔ ∀ x : α, dist (f x) (g x) < C :=
   ⟨fun w x => lt_of_le_of_lt (dist_coe_le_dist x) w, dist_lt_of_nonempty_compact⟩
 #align bounded_continuous_function.dist_lt_iff_of_nonempty_compact BoundedContinuousFunction.dist_lt_iff_of_nonempty_compact
+-/
 
 /-- The type of bounded continuous functions, with the uniform distance, is a pseudometric space. -/
 instance : PseudoMetricSpace (α →ᵇ β)
@@ -249,37 +284,50 @@ instance {α β} [TopologicalSpace α] [MetricSpace β] : MetricSpace (α →ᵇ
     where eq_of_dist_eq_zero f g hfg := by
     ext x <;> exact eq_of_dist_eq_zero (le_antisymm (hfg ▸ dist_coe_le_dist _) dist_nonneg)
 
+#print BoundedContinuousFunction.nndist_eq /-
 theorem nndist_eq : nndist f g = sInf {C | ∀ x : α, nndist (f x) (g x) ≤ C} :=
   Subtype.ext <|
     dist_eq.trans <| by
       rw [NNReal.coe_sInf, NNReal.coe_image]
       simp_rw [mem_set_of_eq, ← NNReal.coe_le_coe, Subtype.coe_mk, exists_prop, coe_nndist]
 #align bounded_continuous_function.nndist_eq BoundedContinuousFunction.nndist_eq
+-/
 
+#print BoundedContinuousFunction.nndist_set_exists /-
 theorem nndist_set_exists : ∃ C, ∀ x : α, nndist (f x) (g x) ≤ C :=
   Subtype.exists.mpr <| dist_set_exists.imp fun a ⟨ha, h⟩ => ⟨ha, h⟩
 #align bounded_continuous_function.nndist_set_exists BoundedContinuousFunction.nndist_set_exists
+-/
 
+#print BoundedContinuousFunction.nndist_coe_le_nndist /-
 theorem nndist_coe_le_nndist (x : α) : nndist (f x) (g x) ≤ nndist f g :=
   dist_coe_le_dist x
 #align bounded_continuous_function.nndist_coe_le_nndist BoundedContinuousFunction.nndist_coe_le_nndist
+-/
 
+#print BoundedContinuousFunction.dist_zero_of_empty /-
 /-- On an empty space, bounded continuous functions are at distance 0 -/
 theorem dist_zero_of_empty [IsEmpty α] : dist f g = 0 := by
   rw [(ext isEmptyElim : f = g), dist_self]
 #align bounded_continuous_function.dist_zero_of_empty BoundedContinuousFunction.dist_zero_of_empty
+-/
 
+#print BoundedContinuousFunction.dist_eq_iSup /-
 theorem dist_eq_iSup : dist f g = ⨆ x : α, dist (f x) (g x) :=
   by
   cases isEmpty_or_nonempty α; · rw [iSup_of_empty', Real.sSup_empty, dist_zero_of_empty]
   refine' (dist_le_iff_of_nonempty.mpr <| le_ciSup _).antisymm (ciSup_le dist_coe_le_dist)
   exact dist_set_exists.imp fun C hC => forall_range_iff.2 hC.2
 #align bounded_continuous_function.dist_eq_supr BoundedContinuousFunction.dist_eq_iSup
+-/
 
+#print BoundedContinuousFunction.nndist_eq_iSup /-
 theorem nndist_eq_iSup : nndist f g = ⨆ x : α, nndist (f x) (g x) :=
   Subtype.ext <| dist_eq_iSup.trans <| by simp_rw [NNReal.coe_iSup, coe_nndist]
 #align bounded_continuous_function.nndist_eq_supr BoundedContinuousFunction.nndist_eq_iSup
+-/
 
+#print BoundedContinuousFunction.tendsto_iff_tendstoUniformly /-
 theorem tendsto_iff_tendstoUniformly {ι : Type _} {F : ι → α →ᵇ β} {f : α →ᵇ β} {l : Filter ι} :
     Tendsto F l (𝓝 f) ↔ TendstoUniformly (fun i => F i) f l :=
   Iff.intro
@@ -296,7 +344,9 @@ theorem tendsto_iff_tendstoUniformly {ι : Type _} {F : ι → α →ᵇ β} {f
             ((dist_le (half_pos ε_pos).le).mpr fun x => dist_comm (f x) (F n x) ▸ le_of_lt (hn x))
             (half_lt_self ε_pos))
 #align bounded_continuous_function.tendsto_iff_tendsto_uniformly BoundedContinuousFunction.tendsto_iff_tendstoUniformly
+-/
 
+#print BoundedContinuousFunction.inducing_coeFn /-
 /-- The topology on `α →ᵇ β` is exactly the topology induced by the natural map to `α →ᵤ β`. -/
 theorem inducing_coeFn : Inducing (UniformFun.ofFun ∘ coeFn : (α →ᵇ β) → α →ᵤ β) :=
   by
@@ -306,11 +356,14 @@ theorem inducing_coeFn : Inducing (UniformFun.ofFun ∘ coeFn : (α →ᵇ β) 
     UniformFun.tendsto_iff_tendstoUniformly]
   rfl
 #align bounded_continuous_function.inducing_coe_fn BoundedContinuousFunction.inducing_coeFn
+-/
 
+#print BoundedContinuousFunction.embedding_coeFn /-
 -- TODO: upgrade to a `uniform_embedding`
 theorem embedding_coeFn : Embedding (UniformFun.ofFun ∘ coeFn : (α →ᵇ β) → α →ᵤ β) :=
   ⟨inducing_coeFn, fun f g h => ext fun x => congr_fun h x⟩
 #align bounded_continuous_function.embedding_coe_fn BoundedContinuousFunction.embedding_coeFn
+-/
 
 variable (α) {β}
 
@@ -324,37 +377,49 @@ def const (b : β) : α →ᵇ β :=
 
 variable {α}
 
+#print BoundedContinuousFunction.const_apply' /-
 theorem const_apply' (a : α) (b : β) : (const α b : α → β) a = b :=
   rfl
 #align bounded_continuous_function.const_apply' BoundedContinuousFunction.const_apply'
+-/
 
 /-- If the target space is inhabited, so is the space of bounded continuous functions -/
 instance [Inhabited β] : Inhabited (α →ᵇ β) :=
   ⟨const α default⟩
 
+#print BoundedContinuousFunction.lipschitz_evalx /-
 theorem lipschitz_evalx (x : α) : LipschitzWith 1 fun f : α →ᵇ β => f x :=
   LipschitzWith.mk_one fun f g => dist_coe_le_dist x
 #align bounded_continuous_function.lipschitz_evalx BoundedContinuousFunction.lipschitz_evalx
+-/
 
+#print BoundedContinuousFunction.uniformContinuous_coe /-
 theorem uniformContinuous_coe : @UniformContinuous (α →ᵇ β) (α → β) _ _ coeFn :=
   uniformContinuous_pi.2 fun x => (lipschitz_evalx x).UniformContinuous
 #align bounded_continuous_function.uniform_continuous_coe BoundedContinuousFunction.uniformContinuous_coe
+-/
 
+#print BoundedContinuousFunction.continuous_coe /-
 theorem continuous_coe : Continuous fun (f : α →ᵇ β) x => f x :=
   UniformContinuous.continuous uniformContinuous_coe
 #align bounded_continuous_function.continuous_coe BoundedContinuousFunction.continuous_coe
+-/
 
+#print BoundedContinuousFunction.continuous_eval_const /-
 /-- When `x` is fixed, `(f : α →ᵇ β) ↦ f x` is continuous -/
 @[continuity]
 theorem continuous_eval_const {x : α} : Continuous fun f : α →ᵇ β => f x :=
   (continuous_apply x).comp continuous_coe
 #align bounded_continuous_function.continuous_eval_const BoundedContinuousFunction.continuous_eval_const
+-/
 
+#print BoundedContinuousFunction.continuous_eval /-
 /-- The evaluation map is continuous, as a joint function of `u` and `x` -/
 @[continuity]
 theorem continuous_eval : Continuous fun p : (α →ᵇ β) × α => p.1 p.2 :=
   (continuous_prod_of_continuous_lipschitz _ 1 fun f => f.Continuous) <| lipschitz_evalx
 #align bounded_continuous_function.continuous_eval BoundedContinuousFunction.continuous_eval
+-/
 
 /-- Bounded continuous functions taking values in a complete space form a complete space. -/
 instance [CompleteSpace β] : CompleteSpace (α →ᵇ β) :=
@@ -402,27 +467,35 @@ def compContinuous {δ : Type _} [TopologicalSpace δ] (f : α →ᵇ β) (g : C
 #align bounded_continuous_function.comp_continuous BoundedContinuousFunction.compContinuous
 -/
 
+#print BoundedContinuousFunction.coe_compContinuous /-
 @[simp]
 theorem coe_compContinuous {δ : Type _} [TopologicalSpace δ] (f : α →ᵇ β) (g : C(δ, α)) :
     coeFn (f.comp_continuous g) = f ∘ g :=
   rfl
 #align bounded_continuous_function.coe_comp_continuous BoundedContinuousFunction.coe_compContinuous
+-/
 
+#print BoundedContinuousFunction.compContinuous_apply /-
 @[simp]
 theorem compContinuous_apply {δ : Type _} [TopologicalSpace δ] (f : α →ᵇ β) (g : C(δ, α)) (x : δ) :
     f.comp_continuous g x = f (g x) :=
   rfl
 #align bounded_continuous_function.comp_continuous_apply BoundedContinuousFunction.compContinuous_apply
+-/
 
+#print BoundedContinuousFunction.lipschitz_compContinuous /-
 theorem lipschitz_compContinuous {δ : Type _} [TopologicalSpace δ] (g : C(δ, α)) :
     LipschitzWith 1 fun f : α →ᵇ β => f.comp_continuous g :=
   LipschitzWith.mk_one fun f₁ f₂ => (dist_le dist_nonneg).2 fun x => dist_coe_le_dist (g x)
 #align bounded_continuous_function.lipschitz_comp_continuous BoundedContinuousFunction.lipschitz_compContinuous
+-/
 
+#print BoundedContinuousFunction.continuous_compContinuous /-
 theorem continuous_compContinuous {δ : Type _} [TopologicalSpace δ] (g : C(δ, α)) :
     Continuous fun f : α →ᵇ β => f.comp_continuous g :=
   (lipschitz_compContinuous g).Continuous
 #align bounded_continuous_function.continuous_comp_continuous BoundedContinuousFunction.continuous_compContinuous
+-/
 
 #print BoundedContinuousFunction.restrict /-
 /-- Restrict a bounded continuous function to a set. -/
@@ -431,15 +504,19 @@ def restrict (f : α →ᵇ β) (s : Set α) : s →ᵇ β :=
 #align bounded_continuous_function.restrict BoundedContinuousFunction.restrict
 -/
 
+#print BoundedContinuousFunction.coe_restrict /-
 @[simp]
 theorem coe_restrict (f : α →ᵇ β) (s : Set α) : coeFn (f.restrict s) = f ∘ coe :=
   rfl
 #align bounded_continuous_function.coe_restrict BoundedContinuousFunction.coe_restrict
+-/
 
+#print BoundedContinuousFunction.restrict_apply /-
 @[simp]
 theorem restrict_apply (f : α →ᵇ β) (s : Set α) (x : s) : f.restrict s x = f x :=
   rfl
 #align bounded_continuous_function.restrict_apply BoundedContinuousFunction.restrict_apply
+-/
 
 #print BoundedContinuousFunction.comp /-
 /-- Composition (in the target) of a bounded continuous function with a Lipschitz map again
@@ -455,6 +532,7 @@ def comp (G : β → γ) {C : ℝ≥0} (H : LipschitzWith C G) (f : α →ᵇ β
 #align bounded_continuous_function.comp BoundedContinuousFunction.comp
 -/
 
+#print BoundedContinuousFunction.lipschitz_comp /-
 /-- The composition operator (in the target) with a Lipschitz map is Lipschitz -/
 theorem lipschitz_comp {G : β → γ} {C : ℝ≥0} (H : LipschitzWith C G) :
     LipschitzWith C (comp G H : (α →ᵇ β) → α →ᵇ γ) :=
@@ -464,23 +542,30 @@ theorem lipschitz_comp {G : β → γ} {C : ℝ≥0} (H : LipschitzWith C G) :
         dist (G (f x)) (G (g x)) ≤ C * dist (f x) (g x) := H.dist_le_mul _ _
         _ ≤ C * dist f g := mul_le_mul_of_nonneg_left (dist_coe_le_dist _) C.2
 #align bounded_continuous_function.lipschitz_comp BoundedContinuousFunction.lipschitz_comp
+-/
 
+#print BoundedContinuousFunction.uniformContinuous_comp /-
 /-- The composition operator (in the target) with a Lipschitz map is uniformly continuous -/
 theorem uniformContinuous_comp {G : β → γ} {C : ℝ≥0} (H : LipschitzWith C G) :
     UniformContinuous (comp G H : (α →ᵇ β) → α →ᵇ γ) :=
   (lipschitz_comp H).UniformContinuous
 #align bounded_continuous_function.uniform_continuous_comp BoundedContinuousFunction.uniformContinuous_comp
+-/
 
+#print BoundedContinuousFunction.continuous_comp /-
 /-- The composition operator (in the target) with a Lipschitz map is continuous -/
 theorem continuous_comp {G : β → γ} {C : ℝ≥0} (H : LipschitzWith C G) :
     Continuous (comp G H : (α →ᵇ β) → α →ᵇ γ) :=
   (lipschitz_comp H).Continuous
 #align bounded_continuous_function.continuous_comp BoundedContinuousFunction.continuous_comp
+-/
 
+#print BoundedContinuousFunction.codRestrict /-
 /-- Restriction (in the target) of a bounded continuous function taking values in a subset -/
 def codRestrict (s : Set β) (f : α →ᵇ β) (H : ∀ x, f x ∈ s) : α →ᵇ s :=
   ⟨⟨s.codRestrict f H, f.Continuous.subtype_mk _⟩, f.Bounded⟩
 #align bounded_continuous_function.cod_restrict BoundedContinuousFunction.codRestrict
+-/
 
 section Extend
 
@@ -500,25 +585,34 @@ def extend (f : α ↪ δ) (g : α →ᵇ β) (h : δ →ᵇ β) : δ →ᵇ β
 #align bounded_continuous_function.extend BoundedContinuousFunction.extend
 -/
 
+#print BoundedContinuousFunction.extend_apply /-
 @[simp]
 theorem extend_apply (f : α ↪ δ) (g : α →ᵇ β) (h : δ →ᵇ β) (x : α) : extend f g h (f x) = g x :=
   f.Injective.extend_apply _ _ _
 #align bounded_continuous_function.extend_apply BoundedContinuousFunction.extend_apply
+-/
 
+#print BoundedContinuousFunction.extend_comp /-
 @[simp]
 theorem extend_comp (f : α ↪ δ) (g : α →ᵇ β) (h : δ →ᵇ β) : extend f g h ∘ f = g :=
   extend_comp f.Injective _ _
 #align bounded_continuous_function.extend_comp BoundedContinuousFunction.extend_comp
+-/
 
+#print BoundedContinuousFunction.extend_apply' /-
 theorem extend_apply' {f : α ↪ δ} {x : δ} (hx : x ∉ range f) (g : α →ᵇ β) (h : δ →ᵇ β) :
     extend f g h x = h x :=
   extend_apply' _ _ _ hx
 #align bounded_continuous_function.extend_apply' BoundedContinuousFunction.extend_apply'
+-/
 
+#print BoundedContinuousFunction.extend_of_empty /-
 theorem extend_of_empty [IsEmpty α] (f : α ↪ δ) (g : α →ᵇ β) (h : δ →ᵇ β) : extend f g h = h :=
   FunLike.coe_injective <| Function.extend_of_isEmpty f g h
 #align bounded_continuous_function.extend_of_empty BoundedContinuousFunction.extend_of_empty
+-/
 
+#print BoundedContinuousFunction.dist_extend_extend /-
 @[simp]
 theorem dist_extend_extend (f : α ↪ δ) (g₁ g₂ : α →ᵇ β) (h₁ h₂ : δ →ᵇ β) :
     dist (g₁.extend f h₁) (g₂.extend f h₂) =
@@ -543,10 +637,13 @@ theorem dist_extend_extend (f : α ↪ δ) (g₁ g₂ : α →ᵇ β) (h₁ h₂
         rw [extend_apply' x.coe_prop, extend_apply' x.coe_prop]
       _ ≤ _ := dist_coe_le_dist _
 #align bounded_continuous_function.dist_extend_extend BoundedContinuousFunction.dist_extend_extend
+-/
 
+#print BoundedContinuousFunction.isometry_extend /-
 theorem isometry_extend (f : α ↪ δ) (h : δ →ᵇ β) : Isometry fun g : α →ᵇ β => extend f g h :=
   Isometry.of_dist_eq fun g₁ g₂ => by simp [dist_nonneg]
 #align bounded_continuous_function.isometry_extend BoundedContinuousFunction.isometry_extend
+-/
 
 end Extend
 
@@ -559,6 +656,7 @@ variable [TopologicalSpace α] [CompactSpace α] [PseudoMetricSpace β]
 variable {f g : α →ᵇ β} {x : α} {C : ℝ}
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (y z «expr ∈ » U) -/
+#print BoundedContinuousFunction.arzela_ascoli₁ /-
 /- Arzela-Ascoli theorem asserts that, on a compact space, a set of functions sharing
 a common modulus of continuity and taking values in a compact set forms a compact
 subset for the topology of uniform convergence. In this section, we prove this theorem
@@ -627,7 +725,9 @@ theorem arzela_ascoli₁ [CompactSpace β] (A : Set (α →ᵇ β)) (closed : Is
       _ < ε₂ + ε₂ := (add_lt_add (hF (f x')).2 (hF (g x')).2)
       _ = ε₁ / 2 := add_halves _
 #align bounded_continuous_function.arzela_ascoli₁ BoundedContinuousFunction.arzela_ascoli₁
+-/
 
+#print BoundedContinuousFunction.arzela_ascoli₂ /-
 /-- Second version, with pointwise equicontinuity and range in a compact subset -/
 theorem arzela_ascoli₂ (s : Set β) (hs : IsCompact s) (A : Set (α →ᵇ β)) (closed : IsClosed A)
     (in_s : ∀ (f : α →ᵇ β) (x : α), f ∈ A → f x ∈ s) (H : Equicontinuous (coeFn : A → α → β)) :
@@ -648,7 +748,9 @@ theorem arzela_ascoli₂ (s : Set β) (hs : IsCompact s) (A : Set (α →ᵇ β)
     rw [show f = F g by ext <;> rfl] at hf ⊢
     exact ⟨g, hf, rfl⟩
 #align bounded_continuous_function.arzela_ascoli₂ BoundedContinuousFunction.arzela_ascoli₂
+-/
 
+#print BoundedContinuousFunction.arzela_ascoli /-
 /-- Third (main) version, with pointwise equicontinuity and range in a compact subset, but
 without closedness. The closure is then compact -/
 theorem arzela_ascoli [T2Space β] (s : Set β) (hs : IsCompact s) (A : Set (α →ᵇ β))
@@ -664,6 +766,7 @@ theorem arzela_ascoli [T2Space β] (s : Set β) (hs : IsCompact s) (A : Set (α
         ⟨g x, in_s g x gA, lt_of_le_of_lt (dist_coe_le_dist _) dist_fg⟩)
     (H.closure' continuous_coe)
 #align bounded_continuous_function.arzela_ascoli BoundedContinuousFunction.arzela_ascoli
+-/
 
 end ArzelaAscoli
 
@@ -675,11 +778,13 @@ variable [TopologicalSpace α] [PseudoMetricSpace β] [One β]
 instance : One (α →ᵇ β) :=
   ⟨const α 1⟩
 
+#print BoundedContinuousFunction.coe_one /-
 @[simp, to_additive]
 theorem coe_one : ((1 : α →ᵇ β) : α → β) = 1 :=
   rfl
 #align bounded_continuous_function.coe_one BoundedContinuousFunction.coe_one
 #align bounded_continuous_function.coe_zero BoundedContinuousFunction.coe_zero
+-/
 
 #print BoundedContinuousFunction.mkOfCompact_one /-
 @[simp, to_additive]
@@ -689,11 +794,13 @@ theorem mkOfCompact_one [CompactSpace α] : mkOfCompact (1 : C(α, β)) = 1 :=
 #align bounded_continuous_function.mk_of_compact_zero BoundedContinuousFunction.mkOfCompact_zero
 -/
 
+#print BoundedContinuousFunction.forall_coe_one_iff_one /-
 @[to_additive]
 theorem forall_coe_one_iff_one (f : α →ᵇ β) : (∀ x, f x = 1) ↔ f = 1 :=
   (@FunLike.ext_iff _ _ _ _ f 1).symm
 #align bounded_continuous_function.forall_coe_one_iff_one BoundedContinuousFunction.forall_coe_one_iff_one
 #align bounded_continuous_function.forall_coe_zero_iff_zero BoundedContinuousFunction.forall_coe_zero_iff_zero
+-/
 
 #print BoundedContinuousFunction.one_compContinuous /-
 @[simp, to_additive]
@@ -738,31 +845,41 @@ instance : Add (α →ᵇ β)
         exact Classical.choose_spec f.bounded x y
         exact Classical.choose_spec g.bounded x y)
 
+#print BoundedContinuousFunction.coe_add /-
 @[simp]
 theorem coe_add : ⇑(f + g) = f + g :=
   rfl
 #align bounded_continuous_function.coe_add BoundedContinuousFunction.coe_add
+-/
 
+#print BoundedContinuousFunction.add_apply /-
 theorem add_apply : (f + g) x = f x + g x :=
   rfl
 #align bounded_continuous_function.add_apply BoundedContinuousFunction.add_apply
+-/
 
+#print BoundedContinuousFunction.mkOfCompact_add /-
 @[simp]
 theorem mkOfCompact_add [CompactSpace α] (f g : C(α, β)) :
     mkOfCompact (f + g) = mkOfCompact f + mkOfCompact g :=
   rfl
 #align bounded_continuous_function.mk_of_compact_add BoundedContinuousFunction.mkOfCompact_add
+-/
 
+#print BoundedContinuousFunction.add_compContinuous /-
 theorem add_compContinuous [TopologicalSpace γ] (h : C(γ, α)) :
     (g + f).comp_continuous h = g.comp_continuous h + f.comp_continuous h :=
   rfl
 #align bounded_continuous_function.add_comp_continuous BoundedContinuousFunction.add_compContinuous
+-/
 
+#print BoundedContinuousFunction.coe_nsmulRec /-
 @[simp]
 theorem coe_nsmulRec : ∀ n, ⇑(nsmulRec n f) = n • f
   | 0 => by rw [nsmulRec, zero_smul, coe_zero]
   | n + 1 => by rw [nsmulRec, succ_nsmul, coe_add, coe_nsmul_rec]
 #align bounded_continuous_function.coe_nsmul_rec BoundedContinuousFunction.coe_nsmulRec
+-/
 
 #print BoundedContinuousFunction.hasNatScalar /-
 instance hasNatScalar : SMul ℕ (α →ᵇ β)
@@ -772,15 +889,19 @@ instance hasNatScalar : SMul ℕ (α →ᵇ β)
 #align bounded_continuous_function.has_nat_scalar BoundedContinuousFunction.hasNatScalar
 -/
 
+#print BoundedContinuousFunction.coe_nsmul /-
 @[simp]
 theorem coe_nsmul (r : ℕ) (f : α →ᵇ β) : ⇑(r • f) = r • f :=
   rfl
 #align bounded_continuous_function.coe_nsmul BoundedContinuousFunction.coe_nsmul
+-/
 
+#print BoundedContinuousFunction.nsmul_apply /-
 @[simp]
 theorem nsmul_apply (r : ℕ) (f : α →ᵇ β) (v : α) : (r • f) v = r • f v :=
   rfl
 #align bounded_continuous_function.nsmul_apply BoundedContinuousFunction.nsmul_apply
+-/
 
 instance : AddMonoid (α →ᵇ β) :=
   FunLike.coe_injective.AddMonoid _ coe_zero coe_add fun _ _ => coe_nsmul _ _
@@ -810,6 +931,7 @@ def coeFnAddHom : (α →ᵇ β) →+ α → β where
 
 variable (α β)
 
+#print BoundedContinuousFunction.toContinuousMapAddHom /-
 /-- The additive map forgetting that a bounded continuous function is bounded.
 -/
 @[simps]
@@ -819,6 +941,7 @@ def toContinuousMapAddHom : (α →ᵇ β) →+ C(α, β)
   map_zero' := by ext; simp
   map_add' := by intros; ext; simp
 #align bounded_continuous_function.to_continuous_map_add_hom BoundedContinuousFunction.toContinuousMapAddHom
+-/
 
 end LipschitzAdd
 
@@ -832,15 +955,19 @@ instance : AddCommMonoid (α →ᵇ β) :=
 
 open scoped BigOperators
 
+#print BoundedContinuousFunction.coe_sum /-
 @[simp]
 theorem coe_sum {ι : Type _} (s : Finset ι) (f : ι → α →ᵇ β) :
     ⇑(∑ i in s, f i) = ∑ i in s, (f i : α → β) :=
   (@coeFnAddHom α β _ _ _ _).map_sum f s
 #align bounded_continuous_function.coe_sum BoundedContinuousFunction.coe_sum
+-/
 
+#print BoundedContinuousFunction.sum_apply /-
 theorem sum_apply {ι : Type _} (s : Finset ι) (f : ι → α →ᵇ β) (a : α) :
     (∑ i in s, f i) a = ∑ i in s, f i a := by simp
 #align bounded_continuous_function.sum_apply BoundedContinuousFunction.sum_apply
+-/
 
 end CommHasLipschitzAdd
 
@@ -856,16 +983,21 @@ variable (f g : α →ᵇ β) {x : α} {C : ℝ}
 instance : Norm (α →ᵇ β) :=
   ⟨fun u => dist u 0⟩
 
+#print BoundedContinuousFunction.norm_def /-
 theorem norm_def : ‖f‖ = dist f 0 :=
   rfl
 #align bounded_continuous_function.norm_def BoundedContinuousFunction.norm_def
+-/
 
+#print BoundedContinuousFunction.norm_eq /-
 /-- The norm of a bounded continuous function is the supremum of `‖f x‖`.
 We use `Inf` to ensure that the definition works if `α` has no elements. -/
 theorem norm_eq (f : α →ᵇ β) : ‖f‖ = sInf {C : ℝ | 0 ≤ C ∧ ∀ x : α, ‖f x‖ ≤ C} := by
   simp [norm_def, BoundedContinuousFunction.dist_eq]
 #align bounded_continuous_function.norm_eq BoundedContinuousFunction.norm_eq
+-/
 
+#print BoundedContinuousFunction.norm_eq_of_nonempty /-
 /-- When the domain is non-empty, we do not need the `0 ≤ C` condition in the formula for ‖f‖ as an
 `Inf`. -/
 theorem norm_eq_of_nonempty [h : Nonempty α] : ‖f‖ = sInf {C : ℝ | ∀ x : α, ‖f x‖ ≤ C} :=
@@ -877,18 +1009,24 @@ theorem norm_eq_of_nonempty [h : Nonempty α] : ‖f‖ = sInf {C : ℝ | ∀ x
   simp only [and_iff_right_iff_imp]
   exact fun h' => le_trans (norm_nonneg (f a)) (h' a)
 #align bounded_continuous_function.norm_eq_of_nonempty BoundedContinuousFunction.norm_eq_of_nonempty
+-/
 
+#print BoundedContinuousFunction.norm_eq_zero_of_empty /-
 @[simp]
 theorem norm_eq_zero_of_empty [h : IsEmpty α] : ‖f‖ = 0 :=
   dist_zero_of_empty
 #align bounded_continuous_function.norm_eq_zero_of_empty BoundedContinuousFunction.norm_eq_zero_of_empty
+-/
 
+#print BoundedContinuousFunction.norm_coe_le_norm /-
 theorem norm_coe_le_norm (x : α) : ‖f x‖ ≤ ‖f‖ :=
   calc
     ‖f x‖ = dist (f x) ((0 : α →ᵇ β) x) := by simp [dist_zero_right]
     _ ≤ ‖f‖ := dist_coe_le_dist _
 #align bounded_continuous_function.norm_coe_le_norm BoundedContinuousFunction.norm_coe_le_norm
+-/
 
+#print BoundedContinuousFunction.dist_le_two_norm' /-
 theorem dist_le_two_norm' {f : γ → β} {C : ℝ} (hC : ∀ x, ‖f x‖ ≤ C) (x y : γ) :
     dist (f x) (f y) ≤ 2 * C :=
   calc
@@ -896,84 +1034,109 @@ theorem dist_le_two_norm' {f : γ → β} {C : ℝ} (hC : ∀ x, ‖f x‖ ≤ C
     _ ≤ C + C := (add_le_add (hC x) (hC y))
     _ = 2 * C := (two_mul _).symm
 #align bounded_continuous_function.dist_le_two_norm' BoundedContinuousFunction.dist_le_two_norm'
+-/
 
+#print BoundedContinuousFunction.dist_le_two_norm /-
 /-- Distance between the images of any two points is at most twice the norm of the function. -/
 theorem dist_le_two_norm (x y : α) : dist (f x) (f y) ≤ 2 * ‖f‖ :=
   dist_le_two_norm' f.norm_coe_le_norm x y
 #align bounded_continuous_function.dist_le_two_norm BoundedContinuousFunction.dist_le_two_norm
+-/
 
 variable {f}
 
+#print BoundedContinuousFunction.norm_le /-
 /-- The norm of a function is controlled by the supremum of the pointwise norms -/
 theorem norm_le (C0 : (0 : ℝ) ≤ C) : ‖f‖ ≤ C ↔ ∀ x : α, ‖f x‖ ≤ C := by
   simpa using @dist_le _ _ _ _ f 0 _ C0
 #align bounded_continuous_function.norm_le BoundedContinuousFunction.norm_le
+-/
 
+#print BoundedContinuousFunction.norm_le_of_nonempty /-
 theorem norm_le_of_nonempty [Nonempty α] {f : α →ᵇ β} {M : ℝ} : ‖f‖ ≤ M ↔ ∀ x, ‖f x‖ ≤ M :=
   by
   simp_rw [norm_def, ← dist_zero_right]
   exact dist_le_iff_of_nonempty
 #align bounded_continuous_function.norm_le_of_nonempty BoundedContinuousFunction.norm_le_of_nonempty
+-/
 
+#print BoundedContinuousFunction.norm_lt_iff_of_compact /-
 theorem norm_lt_iff_of_compact [CompactSpace α] {f : α →ᵇ β} {M : ℝ} (M0 : 0 < M) :
     ‖f‖ < M ↔ ∀ x, ‖f x‖ < M :=
   by
   simp_rw [norm_def, ← dist_zero_right]
   exact dist_lt_iff_of_compact M0
 #align bounded_continuous_function.norm_lt_iff_of_compact BoundedContinuousFunction.norm_lt_iff_of_compact
+-/
 
+#print BoundedContinuousFunction.norm_lt_iff_of_nonempty_compact /-
 theorem norm_lt_iff_of_nonempty_compact [Nonempty α] [CompactSpace α] {f : α →ᵇ β} {M : ℝ} :
     ‖f‖ < M ↔ ∀ x, ‖f x‖ < M :=
   by
   simp_rw [norm_def, ← dist_zero_right]
   exact dist_lt_iff_of_nonempty_compact
 #align bounded_continuous_function.norm_lt_iff_of_nonempty_compact BoundedContinuousFunction.norm_lt_iff_of_nonempty_compact
+-/
 
 variable (f)
 
+#print BoundedContinuousFunction.norm_const_le /-
 /-- Norm of `const α b` is less than or equal to `‖b‖`. If `α` is nonempty,
 then it is equal to `‖b‖`. -/
 theorem norm_const_le (b : β) : ‖const α b‖ ≤ ‖b‖ :=
   (norm_le (norm_nonneg b)).2 fun x => le_rfl
 #align bounded_continuous_function.norm_const_le BoundedContinuousFunction.norm_const_le
+-/
 
+#print BoundedContinuousFunction.norm_const_eq /-
 @[simp]
 theorem norm_const_eq [h : Nonempty α] (b : β) : ‖const α b‖ = ‖b‖ :=
   le_antisymm (norm_const_le b) <| h.elim fun x => (const α b).norm_coe_le_norm x
 #align bounded_continuous_function.norm_const_eq BoundedContinuousFunction.norm_const_eq
+-/
 
+#print BoundedContinuousFunction.ofNormedAddCommGroup /-
 /-- Constructing a bounded continuous function from a uniformly bounded continuous
 function taking values in a normed group. -/
 def ofNormedAddCommGroup {α : Type u} {β : Type v} [TopologicalSpace α] [SeminormedAddCommGroup β]
     (f : α → β) (Hf : Continuous f) (C : ℝ) (H : ∀ x, ‖f x‖ ≤ C) : α →ᵇ β :=
   ⟨⟨fun n => f n, Hf⟩, ⟨_, dist_le_two_norm' H⟩⟩
 #align bounded_continuous_function.of_normed_add_comm_group BoundedContinuousFunction.ofNormedAddCommGroup
+-/
 
+#print BoundedContinuousFunction.coe_ofNormedAddCommGroup /-
 @[simp]
 theorem coe_ofNormedAddCommGroup {α : Type u} {β : Type v} [TopologicalSpace α]
     [SeminormedAddCommGroup β] (f : α → β) (Hf : Continuous f) (C : ℝ) (H : ∀ x, ‖f x‖ ≤ C) :
     (ofNormedAddCommGroup f Hf C H : α → β) = f :=
   rfl
 #align bounded_continuous_function.coe_of_normed_add_comm_group BoundedContinuousFunction.coe_ofNormedAddCommGroup
+-/
 
+#print BoundedContinuousFunction.norm_ofNormedAddCommGroup_le /-
 theorem norm_ofNormedAddCommGroup_le {f : α → β} (hfc : Continuous f) {C : ℝ} (hC : 0 ≤ C)
     (hfC : ∀ x, ‖f x‖ ≤ C) : ‖ofNormedAddCommGroup f hfc C hfC‖ ≤ C :=
   (norm_le hC).2 hfC
 #align bounded_continuous_function.norm_of_normed_add_comm_group_le BoundedContinuousFunction.norm_ofNormedAddCommGroup_le
+-/
 
+#print BoundedContinuousFunction.ofNormedAddCommGroupDiscrete /-
 /-- Constructing a bounded continuous function from a uniformly bounded
 function on a discrete space, taking values in a normed group -/
 def ofNormedAddCommGroupDiscrete {α : Type u} {β : Type v} [TopologicalSpace α] [DiscreteTopology α]
     [SeminormedAddCommGroup β] (f : α → β) (C : ℝ) (H : ∀ x, norm (f x) ≤ C) : α →ᵇ β :=
   ofNormedAddCommGroup f continuous_of_discreteTopology C H
 #align bounded_continuous_function.of_normed_add_comm_group_discrete BoundedContinuousFunction.ofNormedAddCommGroupDiscrete
+-/
 
+#print BoundedContinuousFunction.coe_ofNormedAddCommGroupDiscrete /-
 @[simp]
 theorem coe_ofNormedAddCommGroupDiscrete {α : Type u} {β : Type v} [TopologicalSpace α]
     [DiscreteTopology α] [SeminormedAddCommGroup β] (f : α → β) (C : ℝ) (H : ∀ x, ‖f x‖ ≤ C) :
     (ofNormedAddCommGroupDiscrete f C H : α → β) = f :=
   rfl
 #align bounded_continuous_function.coe_of_normed_add_comm_group_discrete BoundedContinuousFunction.coe_ofNormedAddCommGroupDiscrete
+-/
 
 #print BoundedContinuousFunction.normComp /-
 /-- Taking the pointwise norm of a bounded continuous function with values in a
@@ -983,22 +1146,30 @@ def normComp : α →ᵇ ℝ :=
 #align bounded_continuous_function.norm_comp BoundedContinuousFunction.normComp
 -/
 
+#print BoundedContinuousFunction.coe_normComp /-
 @[simp]
 theorem coe_normComp : (f.normComp : α → ℝ) = norm ∘ f :=
   rfl
 #align bounded_continuous_function.coe_norm_comp BoundedContinuousFunction.coe_normComp
+-/
 
+#print BoundedContinuousFunction.norm_normComp /-
 @[simp]
 theorem norm_normComp : ‖f.normComp‖ = ‖f‖ := by simp only [norm_eq, coe_norm_comp, norm_norm]
 #align bounded_continuous_function.norm_norm_comp BoundedContinuousFunction.norm_normComp
+-/
 
+#print BoundedContinuousFunction.bddAbove_range_norm_comp /-
 theorem bddAbove_range_norm_comp : BddAbove <| Set.range <| norm ∘ f :=
   (Real.bounded_iff_bddBelow_bddAbove.mp <| @bounded_range _ _ _ _ f.normComp).2
 #align bounded_continuous_function.bdd_above_range_norm_comp BoundedContinuousFunction.bddAbove_range_norm_comp
+-/
 
+#print BoundedContinuousFunction.norm_eq_iSup_norm /-
 theorem norm_eq_iSup_norm : ‖f‖ = ⨆ x : α, ‖f x‖ := by
   simp_rw [norm_def, dist_eq_supr, coe_zero, Pi.zero_apply, dist_zero_right]
 #align bounded_continuous_function.norm_eq_supr_norm BoundedContinuousFunction.norm_eq_iSup_norm
+-/
 
 /-- If `‖(1 : β)‖ = 1`, then `‖(1 : α →ᵇ β)‖ = 1` if `α` is nonempty. -/
 instance [Nonempty α] [One β] [NormOneClass β] : NormOneClass (α →ᵇ β)
@@ -1021,40 +1192,54 @@ instance : Sub (α →ᵇ β) :=
           (add_le_add (f.norm_coe_le_norm x) <|
             trans_rel_right _ (norm_neg _) (g.norm_coe_le_norm x))⟩
 
+#print BoundedContinuousFunction.coe_neg /-
 @[simp]
 theorem coe_neg : ⇑(-f) = -f :=
   rfl
 #align bounded_continuous_function.coe_neg BoundedContinuousFunction.coe_neg
+-/
 
+#print BoundedContinuousFunction.neg_apply /-
 theorem neg_apply : (-f) x = -f x :=
   rfl
 #align bounded_continuous_function.neg_apply BoundedContinuousFunction.neg_apply
+-/
 
+#print BoundedContinuousFunction.coe_sub /-
 @[simp]
 theorem coe_sub : ⇑(f - g) = f - g :=
   rfl
 #align bounded_continuous_function.coe_sub BoundedContinuousFunction.coe_sub
+-/
 
+#print BoundedContinuousFunction.sub_apply /-
 theorem sub_apply : (f - g) x = f x - g x :=
   rfl
 #align bounded_continuous_function.sub_apply BoundedContinuousFunction.sub_apply
+-/
 
+#print BoundedContinuousFunction.mkOfCompact_neg /-
 @[simp]
 theorem mkOfCompact_neg [CompactSpace α] (f : C(α, β)) : mkOfCompact (-f) = -mkOfCompact f :=
   rfl
 #align bounded_continuous_function.mk_of_compact_neg BoundedContinuousFunction.mkOfCompact_neg
+-/
 
+#print BoundedContinuousFunction.mkOfCompact_sub /-
 @[simp]
 theorem mkOfCompact_sub [CompactSpace α] (f g : C(α, β)) :
     mkOfCompact (f - g) = mkOfCompact f - mkOfCompact g :=
   rfl
 #align bounded_continuous_function.mk_of_compact_sub BoundedContinuousFunction.mkOfCompact_sub
+-/
 
+#print BoundedContinuousFunction.coe_zsmulRec /-
 @[simp]
 theorem coe_zsmulRec : ∀ z, ⇑(zsmulRec z f) = z • f
   | Int.ofNat n => by rw [zsmulRec, Int.ofNat_eq_coe, coe_nsmul_rec, coe_nat_zsmul]
   | -[n+1] => by rw [zsmulRec, negSucc_zsmul, coe_neg, coe_nsmul_rec]
 #align bounded_continuous_function.coe_zsmul_rec BoundedContinuousFunction.coe_zsmulRec
+-/
 
 #print BoundedContinuousFunction.hasIntScalar /-
 instance hasIntScalar : SMul ℤ (α →ᵇ β)
@@ -1064,15 +1249,19 @@ instance hasIntScalar : SMul ℤ (α →ᵇ β)
 #align bounded_continuous_function.has_int_scalar BoundedContinuousFunction.hasIntScalar
 -/
 
+#print BoundedContinuousFunction.coe_zsmul /-
 @[simp]
 theorem coe_zsmul (r : ℤ) (f : α →ᵇ β) : ⇑(r • f) = r • f :=
   rfl
 #align bounded_continuous_function.coe_zsmul BoundedContinuousFunction.coe_zsmul
+-/
 
+#print BoundedContinuousFunction.zsmul_apply /-
 @[simp]
 theorem zsmul_apply (r : ℤ) (f : α →ᵇ β) (v : α) : (r • f) v = r • f v :=
   rfl
 #align bounded_continuous_function.zsmul_apply BoundedContinuousFunction.zsmul_apply
+-/
 
 instance : AddCommGroup (α →ᵇ β) :=
   FunLike.coe_injective.AddCommGroup _ coe_zero coe_add coe_neg coe_sub (fun _ _ => coe_nsmul _ _)
@@ -1084,22 +1273,30 @@ instance : SeminormedAddCommGroup (α →ᵇ β)
 instance {α β} [TopologicalSpace α] [NormedAddCommGroup β] : NormedAddCommGroup (α →ᵇ β) :=
   { BoundedContinuousFunction.seminormedAddCommGroup with }
 
+#print BoundedContinuousFunction.nnnorm_def /-
 theorem nnnorm_def : ‖f‖₊ = nndist f 0 :=
   rfl
 #align bounded_continuous_function.nnnorm_def BoundedContinuousFunction.nnnorm_def
+-/
 
+#print BoundedContinuousFunction.nnnorm_coe_le_nnnorm /-
 theorem nnnorm_coe_le_nnnorm (x : α) : ‖f x‖₊ ≤ ‖f‖₊ :=
   norm_coe_le_norm _ _
 #align bounded_continuous_function.nnnorm_coe_le_nnnorm BoundedContinuousFunction.nnnorm_coe_le_nnnorm
+-/
 
+#print BoundedContinuousFunction.nndist_le_two_nnnorm /-
 theorem nndist_le_two_nnnorm (x y : α) : nndist (f x) (f y) ≤ 2 * ‖f‖₊ :=
   dist_le_two_norm _ _ _
 #align bounded_continuous_function.nndist_le_two_nnnorm BoundedContinuousFunction.nndist_le_two_nnnorm
+-/
 
+#print BoundedContinuousFunction.nnnorm_le /-
 /-- The nnnorm of a function is controlled by the supremum of the pointwise nnnorms -/
 theorem nnnorm_le (C : ℝ≥0) : ‖f‖₊ ≤ C ↔ ∀ x : α, ‖f x‖₊ ≤ C :=
   norm_le C.Prop
 #align bounded_continuous_function.nnnorm_le BoundedContinuousFunction.nnnorm_le
+-/
 
 #print BoundedContinuousFunction.nnnorm_const_le /-
 theorem nnnorm_const_le (b : β) : ‖const α b‖₊ ≤ ‖b‖₊ :=
@@ -1114,23 +1311,31 @@ theorem nnnorm_const_eq [h : Nonempty α] (b : β) : ‖const α b‖₊ = ‖b
 #align bounded_continuous_function.nnnorm_const_eq BoundedContinuousFunction.nnnorm_const_eq
 -/
 
+#print BoundedContinuousFunction.nnnorm_eq_iSup_nnnorm /-
 theorem nnnorm_eq_iSup_nnnorm : ‖f‖₊ = ⨆ x : α, ‖f x‖₊ :=
   Subtype.ext <| (norm_eq_iSup_norm f).trans <| by simp_rw [NNReal.coe_iSup, coe_nnnorm]
 #align bounded_continuous_function.nnnorm_eq_supr_nnnorm BoundedContinuousFunction.nnnorm_eq_iSup_nnnorm
+-/
 
+#print BoundedContinuousFunction.abs_diff_coe_le_dist /-
 theorem abs_diff_coe_le_dist : ‖f x - g x‖ ≤ dist f g := by rw [dist_eq_norm];
   exact (f - g).norm_coe_le_norm x
 #align bounded_continuous_function.abs_diff_coe_le_dist BoundedContinuousFunction.abs_diff_coe_le_dist
+-/
 
+#print BoundedContinuousFunction.coe_le_coe_add_dist /-
 theorem coe_le_coe_add_dist {f g : α →ᵇ ℝ} : f x ≤ g x + dist f g :=
   sub_le_iff_le_add'.1 <| (abs_le.1 <| @dist_coe_le_dist _ _ _ _ f g x).2
 #align bounded_continuous_function.coe_le_coe_add_dist BoundedContinuousFunction.coe_le_coe_add_dist
+-/
 
+#print BoundedContinuousFunction.norm_compContinuous_le /-
 theorem norm_compContinuous_le [TopologicalSpace γ] (f : α →ᵇ β) (g : C(γ, α)) :
     ‖f.comp_continuous g‖ ≤ ‖f‖ :=
   ((lipschitz_compContinuous g).dist_le_mul f 0).trans <| by
     rw [NNReal.coe_one, one_mul, dist_zero_right]
 #align bounded_continuous_function.norm_comp_continuous_le BoundedContinuousFunction.norm_compContinuous_le
+-/
 
 end NormedAddCommGroup
 
@@ -1163,14 +1368,18 @@ instance : SMul 𝕜 (α →ᵇ β)
           refine' mul_le_mul_of_nonneg_left _ dist_nonneg
           exact hb x y⟩ }
 
+#print BoundedContinuousFunction.coe_smul /-
 @[simp]
 theorem coe_smul (c : 𝕜) (f : α →ᵇ β) : ⇑(c • f) = fun x => c • f x :=
   rfl
 #align bounded_continuous_function.coe_smul BoundedContinuousFunction.coe_smul
+-/
 
+#print BoundedContinuousFunction.smul_apply /-
 theorem smul_apply (c : 𝕜) (f : α →ᵇ β) (x : α) : (c • f) x = c • f x :=
   rfl
 #align bounded_continuous_function.smul_apply BoundedContinuousFunction.smul_apply
+-/
 
 instance [SMul 𝕜ᵐᵒᵖ β] [IsCentralScalar 𝕜 β] : IsCentralScalar 𝕜 (α →ᵇ β)
     where op_smul_eq_smul _ _ := ext fun _ => op_smul_eq_smul _ _
@@ -1226,20 +1435,25 @@ instance : Module 𝕜 (α →ᵇ β) :=
 
 variable (𝕜)
 
+#print BoundedContinuousFunction.evalClm /-
 /-- The evaluation at a point, as a continuous linear map from `α →ᵇ β` to `β`. -/
 def evalClm (x : α) : (α →ᵇ β) →L[𝕜] β where
   toFun f := f x
   map_add' f g := add_apply _ _
   map_smul' c f := smul_apply _ _ _
 #align bounded_continuous_function.eval_clm BoundedContinuousFunction.evalClm
+-/
 
+#print BoundedContinuousFunction.evalClm_apply /-
 @[simp]
 theorem evalClm_apply (x : α) (f : α →ᵇ β) : evalClm 𝕜 x f = f x :=
   rfl
 #align bounded_continuous_function.eval_clm_apply BoundedContinuousFunction.evalClm_apply
+-/
 
 variable (α β)
 
+#print BoundedContinuousFunction.toContinuousMapLinearMap /-
 /-- The linear map forgetting that a bounded continuous function is bounded. -/
 @[simps]
 def toContinuousMapLinearMap : (α →ᵇ β) →ₗ[𝕜] C(α, β)
@@ -1248,6 +1462,7 @@ def toContinuousMapLinearMap : (α →ᵇ β) →ₗ[𝕜] C(α, β)
   map_smul' f g := rfl
   map_add' c f := rfl
 #align bounded_continuous_function.to_continuous_map_linear_map BoundedContinuousFunction.toContinuousMapLinearMap
+-/
 
 end Module
 
@@ -1283,6 +1498,7 @@ variable [SeminormedAddCommGroup γ] [NormedSpace 𝕜 γ]
 
 variable (α)
 
+#print ContinuousLinearMap.compLeftContinuousBounded /-
 -- TODO does this work in the `has_bounded_smul` setting, too?
 /--
 Postcomposition of bounded continuous functions into a normed module by a continuous linear map is
@@ -1299,12 +1515,15 @@ protected def ContinuousLinearMap.compLeftContinuousBounded (g : β →L[𝕜] 
       map_smul' := fun c f => by ext <;> simp } ‖g‖ fun f =>
     norm_ofNormedAddCommGroup_le _ (mul_nonneg (norm_nonneg g) (norm_nonneg f)) _
 #align continuous_linear_map.comp_left_continuous_bounded ContinuousLinearMap.compLeftContinuousBounded
+-/
 
+#print ContinuousLinearMap.compLeftContinuousBounded_apply /-
 @[simp]
 theorem ContinuousLinearMap.compLeftContinuousBounded_apply (g : β →L[𝕜] γ) (f : α →ᵇ β) (x : α) :
     (g.compLeftContinuousBounded α f) x = g (f x) :=
   rfl
 #align continuous_linear_map.comp_left_continuous_bounded_apply ContinuousLinearMap.compLeftContinuousBounded_apply
+-/
 
 end NormedSpace
 
@@ -1332,14 +1551,18 @@ instance : Mul (α →ᵇ R)
       le_trans (norm_mul_le (f x) (g x)) <|
         mul_le_mul (f.norm_coe_le_norm x) (g.norm_coe_le_norm x) (norm_nonneg _) (norm_nonneg _)
 
+#print BoundedContinuousFunction.coe_mul /-
 @[simp]
 theorem coe_mul (f g : α →ᵇ R) : ⇑(f * g) = f * g :=
   rfl
 #align bounded_continuous_function.coe_mul BoundedContinuousFunction.coe_mul
+-/
 
+#print BoundedContinuousFunction.mul_apply /-
 theorem mul_apply (f g : α →ᵇ R) (x : α) : (f * g) x = f x * g x :=
   rfl
 #align bounded_continuous_function.mul_apply BoundedContinuousFunction.mul_apply
+-/
 
 instance : NonUnitalRing (α →ᵇ R) :=
   FunLike.coe_injective.NonUnitalRing _ coe_zero coe_add coe_mul coe_neg coe_sub
@@ -1362,11 +1585,13 @@ section SemiNormed
 
 variable [SeminormedRing R]
 
+#print BoundedContinuousFunction.coe_npowRec /-
 @[simp]
 theorem coe_npowRec (f : α →ᵇ R) : ∀ n, ⇑(npowRec n f) = f ^ n
   | 0 => by rw [npowRec, pow_zero, coe_one]
   | n + 1 => by rw [npowRec, pow_succ, coe_mul, coe_npow_rec]
 #align bounded_continuous_function.coe_npow_rec BoundedContinuousFunction.coe_npowRec
+-/
 
 #print BoundedContinuousFunction.hasNatPow /-
 instance hasNatPow : Pow (α →ᵇ R) ℕ
@@ -1376,31 +1601,39 @@ instance hasNatPow : Pow (α →ᵇ R) ℕ
 #align bounded_continuous_function.has_nat_pow BoundedContinuousFunction.hasNatPow
 -/
 
+#print BoundedContinuousFunction.coe_pow /-
 @[simp]
 theorem coe_pow (n : ℕ) (f : α →ᵇ R) : ⇑(f ^ n) = f ^ n :=
   rfl
 #align bounded_continuous_function.coe_pow BoundedContinuousFunction.coe_pow
+-/
 
+#print BoundedContinuousFunction.pow_apply /-
 @[simp]
 theorem pow_apply (n : ℕ) (f : α →ᵇ R) (v : α) : (f ^ n) v = f v ^ n :=
   rfl
 #align bounded_continuous_function.pow_apply BoundedContinuousFunction.pow_apply
+-/
 
 instance : NatCast (α →ᵇ R) :=
   ⟨fun n => BoundedContinuousFunction.const _ n⟩
 
+#print BoundedContinuousFunction.coe_natCast /-
 @[simp, norm_cast]
 theorem coe_natCast (n : ℕ) : ((n : α →ᵇ R) : α → R) = n :=
   rfl
 #align bounded_continuous_function.coe_nat_cast BoundedContinuousFunction.coe_natCast
+-/
 
 instance : IntCast (α →ᵇ R) :=
   ⟨fun n => BoundedContinuousFunction.const _ n⟩
 
+#print BoundedContinuousFunction.coe_intCast /-
 @[simp, norm_cast]
 theorem coe_intCast (n : ℤ) : ((n : α →ᵇ R) : α → R) = n :=
   rfl
 #align bounded_continuous_function.coe_int_cast BoundedContinuousFunction.coe_intCast
+-/
 
 instance : Ring (α →ᵇ R) :=
   FunLike.coe_injective.Ring _ coe_zero coe_one coe_add coe_mul coe_neg coe_sub
@@ -1476,10 +1709,12 @@ instance : Algebra 𝕜 (α →ᵇ γ) :=
     commutes' := fun c f => ext fun x => Algebra.commutes' _ _
     smul_def' := fun c f => ext fun x => Algebra.smul_def' _ _ }
 
+#print BoundedContinuousFunction.algebraMap_apply /-
 @[simp]
 theorem algebraMap_apply (k : 𝕜) (a : α) : algebraMap 𝕜 (α →ᵇ γ) k a = k • 1 := by
   rw [Algebra.algebraMap_eq_smul_one]; rfl
 #align bounded_continuous_function.algebra_map_apply BoundedContinuousFunction.algebraMap_apply
+-/
 
 instance : NormedAlgebra 𝕜 (α →ᵇ γ) :=
   { BoundedContinuousFunction.normedSpace with }
@@ -1503,6 +1738,7 @@ instance hasSmul' : SMul (α →ᵇ 𝕜) (α →ᵇ β) :=
 #align bounded_continuous_function.has_smul' BoundedContinuousFunction.hasSmul'
 -/
 
+#print BoundedContinuousFunction.module' /-
 instance module' : Module (α →ᵇ 𝕜) (α →ᵇ β) :=
   Module.ofCore <|
     { smul := (· • ·)
@@ -1511,16 +1747,20 @@ instance module' : Module (α →ᵇ 𝕜) (α →ᵇ β) :=
       mul_smul := fun c₁ c₂ f => ext fun x => mul_smul _ _ _
       one_smul := fun f => ext fun x => one_smul 𝕜 (f x) }
 #align bounded_continuous_function.module' BoundedContinuousFunction.module'
+-/
 
+#print BoundedContinuousFunction.norm_smul_le /-
 theorem norm_smul_le (f : α →ᵇ 𝕜) (g : α →ᵇ β) : ‖f • g‖ ≤ ‖f‖ * ‖g‖ :=
   norm_ofNormedAddCommGroup_le _ (mul_nonneg (norm_nonneg _) (norm_nonneg _)) _
 #align bounded_continuous_function.norm_smul_le BoundedContinuousFunction.norm_smul_le
+-/
 
 /- TODO: When `normed_module` has been added to `normed_space.basic`, the above facts
 show that the space of bounded continuous functions from `α` to `β` is naturally a normed
 module over the algebra of bounded continuous functions from `α` to `𝕜`. -/
 end NormedAlgebra
 
+#print BoundedContinuousFunction.Nnreal.upper_bound /-
 theorem Nnreal.upper_bound {α : Type _} [TopologicalSpace α] (f : α →ᵇ ℝ≥0) (x : α) :
     f x ≤ nndist f 0 :=
   by
@@ -1528,6 +1768,7 @@ theorem Nnreal.upper_bound {α : Type _} [TopologicalSpace α] (f : α →ᵇ 
   simp only [coe_zero, Pi.zero_apply] at key 
   rwa [NNReal.nndist_zero_eq_val' (f x)] at key 
 #align bounded_continuous_function.nnreal.upper_bound BoundedContinuousFunction.Nnreal.upper_bound
+-/
 
 /-!
 ### Star structures
@@ -1560,17 +1801,21 @@ instance : StarAddMonoid (α →ᵇ β)
   star_involutive f := ext fun x => star_star (f x)
   star_add f g := ext fun x => star_add (f x) (g x)
 
+#print BoundedContinuousFunction.coe_star /-
 /-- The right-hand side of this equality can be parsed `star ∘ ⇑f` because of the
 instance `pi.has_star`. Upon inspecting the goal, one sees `⊢ ⇑(star f) = star ⇑f`.-/
 @[simp]
 theorem coe_star (f : α →ᵇ β) : ⇑(star f) = star f :=
   rfl
 #align bounded_continuous_function.coe_star BoundedContinuousFunction.coe_star
+-/
 
+#print BoundedContinuousFunction.star_apply /-
 @[simp]
 theorem star_apply (f : α →ᵇ β) (x : α) : star f x = star (f x) :=
   rfl
 #align bounded_continuous_function.star_apply BoundedContinuousFunction.star_apply
+-/
 
 instance : NormedStarGroup (α →ᵇ β)
     where norm_star f := by simp only [norm_eq, star_apply, norm_star]
@@ -1657,15 +1902,19 @@ instance : SemilatticeSup (α →ᵇ β) :=
 instance : Lattice (α →ᵇ β) :=
   { BoundedContinuousFunction.semilatticeSup, BoundedContinuousFunction.semilatticeInf with }
 
+#print BoundedContinuousFunction.coeFn_sup /-
 @[simp]
 theorem coeFn_sup (f g : α →ᵇ β) : ⇑(f ⊔ g) = f ⊔ g :=
   rfl
 #align bounded_continuous_function.coe_fn_sup BoundedContinuousFunction.coeFn_sup
+-/
 
+#print BoundedContinuousFunction.coeFn_abs /-
 @[simp]
 theorem coeFn_abs (f : α →ᵇ β) : ⇑(|f|) = |f| :=
   rfl
 #align bounded_continuous_function.coe_fn_abs BoundedContinuousFunction.coeFn_abs
+-/
 
 instance : NormedLatticeAddCommGroup (α →ᵇ β) :=
   { BoundedContinuousFunction.lattice,
@@ -1687,41 +1936,53 @@ section NonnegativePart
 
 variable [TopologicalSpace α]
 
+#print BoundedContinuousFunction.nnrealPart /-
 /-- The nonnegative part of a bounded continuous `ℝ`-valued function as a bounded
 continuous `ℝ≥0`-valued function. -/
 def nnrealPart (f : α →ᵇ ℝ) : α →ᵇ ℝ≥0 :=
   BoundedContinuousFunction.comp _ (show LipschitzWith 1 Real.toNNReal from lipschitzWith_pos) f
 #align bounded_continuous_function.nnreal_part BoundedContinuousFunction.nnrealPart
+-/
 
+#print BoundedContinuousFunction.nnrealPart_coeFn_eq /-
 @[simp]
 theorem nnrealPart_coeFn_eq (f : α →ᵇ ℝ) : ⇑f.nnrealPart = Real.toNNReal ∘ ⇑f :=
   rfl
 #align bounded_continuous_function.nnreal_part_coe_fun_eq BoundedContinuousFunction.nnrealPart_coeFn_eq
+-/
 
+#print BoundedContinuousFunction.nnnorm /-
 /-- The absolute value of a bounded continuous `ℝ`-valued function as a bounded
 continuous `ℝ≥0`-valued function. -/
 def nnnorm (f : α →ᵇ ℝ) : α →ᵇ ℝ≥0 :=
   BoundedContinuousFunction.comp _
     (show LipschitzWith 1 fun x : ℝ => ‖x‖₊ from lipschitzWith_one_norm) f
 #align bounded_continuous_function.nnnorm BoundedContinuousFunction.nnnorm
+-/
 
+#print BoundedContinuousFunction.nnnorm_coeFn_eq /-
 @[simp]
 theorem nnnorm_coeFn_eq (f : α →ᵇ ℝ) : ⇑f.nnnorm = NNNorm.nnnorm ∘ ⇑f :=
   rfl
 #align bounded_continuous_function.nnnorm_coe_fun_eq BoundedContinuousFunction.nnnorm_coeFn_eq
+-/
 
+#print BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_neg /-
 /-- Decompose a bounded continuous function to its positive and negative parts. -/
 theorem self_eq_nnrealPart_sub_nnrealPart_neg (f : α →ᵇ ℝ) :
     ⇑f = coe ∘ f.nnrealPart - coe ∘ (-f).nnrealPart := by funext x; dsimp;
   simp only [max_zero_sub_max_neg_zero_eq_self]
 #align bounded_continuous_function.self_eq_nnreal_part_sub_nnreal_part_neg BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_neg
+-/
 
+#print BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_neg /-
 /-- Express the absolute value of a bounded continuous function in terms of its
 positive and negative parts. -/
 theorem abs_self_eq_nnrealPart_add_nnrealPart_neg (f : α →ᵇ ℝ) :
     abs ∘ ⇑f = coe ∘ f.nnrealPart + coe ∘ (-f).nnrealPart := by funext x; dsimp;
   simp only [max_zero_add_max_neg_zero_eq_abs_self]
 #align bounded_continuous_function.abs_self_eq_nnreal_part_add_nnreal_part_neg BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_neg
+-/
 
 end NonnegativePart
 

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

@@ -389,7 +389,6 @@ instance [CompleteSpace β] : CompleteSpace (α →ᵇ β) :=
         dist (F x) (F y) ≤ dist (f 0 x) (f 0 y) + (dist (f 0 x) (F x) + dist (f 0 y) (F y)) :=
           dist_triangle4_left _ _ _ _
         _ ≤ C + (b 0 + b 0) := by mono*
-        
     · -- Check that `F` is close to `f N` in distance terms
       refine' tendsto_iff_dist_tendsto_zero.2 (squeeze_zero (fun _ => dist_nonneg) _ b_lim)
       exact fun N => (dist_le (b0 _)).2 fun x => fF_bdd x N
@@ -452,8 +451,7 @@ def comp (G : β → γ) {C : ℝ≥0} (H : LipschitzWith C G) (f : α →ᵇ β
       calc
         dist (G (f x)) (G (f y)) ≤ C * dist (f x) (f y) := H.dist_le_mul _ _
         _ ≤ max C 0 * dist (f x) (f y) := (mul_le_mul_of_nonneg_right (le_max_left C 0) dist_nonneg)
-        _ ≤ max C 0 * D := mul_le_mul_of_nonneg_left (hD _ _) (le_max_right C 0)
-        ⟩⟩
+        _ ≤ max C 0 * D := mul_le_mul_of_nonneg_left (hD _ _) (le_max_right C 0)⟩⟩
 #align bounded_continuous_function.comp BoundedContinuousFunction.comp
 -/
 
@@ -465,7 +463,6 @@ theorem lipschitz_comp {G : β → γ} {C : ℝ≥0} (H : LipschitzWith C G) :
       calc
         dist (G (f x)) (G (g x)) ≤ C * dist (f x) (g x) := H.dist_le_mul _ _
         _ ≤ C * dist f g := mul_le_mul_of_nonneg_left (dist_coe_le_dist _) C.2
-        
 #align bounded_continuous_function.lipschitz_comp BoundedContinuousFunction.lipschitz_comp
 
 /-- The composition operator (in the target) with a Lipschitz map is uniformly continuous -/
@@ -537,7 +534,6 @@ theorem dist_extend_extend (f : α ↪ δ) (g₁ g₂ : α →ᵇ β) (h₁ h₂
         dist (h₁ x) (h₂ x) = dist (h₁.restrict (range fᶜ) x) (h₂.restrict (range fᶜ) x) := rfl
         _ ≤ dist (h₁.restrict (range fᶜ)) (h₂.restrict (range fᶜ)) := (dist_coe_le_dist x)
         _ ≤ _ := le_max_right _ _
-        
   · refine' (dist_le dist_nonneg).2 fun x => _
     rw [← extend_apply f g₁ h₁, ← extend_apply f g₂ h₂]
     exact dist_coe_le_dist _
@@ -546,7 +542,6 @@ theorem dist_extend_extend (f : α ↪ δ) (g₁ g₂ : α →ᵇ β) (h₁ h₂
       dist (h₁ x) (h₂ x) = dist (extend f g₁ h₁ x) (extend f g₂ h₂ x) := by
         rw [extend_apply' x.coe_prop, extend_apply' x.coe_prop]
       _ ≤ _ := dist_coe_le_dist _
-      
 #align bounded_continuous_function.dist_extend_extend BoundedContinuousFunction.dist_extend_extend
 
 theorem isometry_extend (f : α ↪ δ) (h : δ →ᵇ β) : Isometry fun g : α →ᵇ β => extend f g h :=
@@ -621,7 +616,6 @@ theorem arzela_ascoli₁ [CompactSpace β] (A : Set (α →ᵇ β)) (closed : Is
       dist_triangle4_right _ _ _ _
     _ ≤ ε₂ + ε₂ + ε₁ / 2 := (le_of_lt (add_lt_add (add_lt_add _ _) _))
     _ = ε₁ := by rw [add_halves, add_halves]
-    
   · exact (hU x').2.2 _ hx' _ (hU x').1 hf
   · exact (hU x').2.2 _ hx' _ (hU x').1 hg
   · have F_f_g : F (f x') = F (g x') :=
@@ -632,7 +626,6 @@ theorem arzela_ascoli₁ [CompactSpace β] (A : Set (α →ᵇ β)) (closed : Is
       _ = dist (f x') (F (f x')) + dist (g x') (F (g x')) := by rw [F_f_g]
       _ < ε₂ + ε₂ := (add_lt_add (hF (f x')).2 (hF (g x')).2)
       _ = ε₁ / 2 := add_halves _
-      
 #align bounded_continuous_function.arzela_ascoli₁ BoundedContinuousFunction.arzela_ascoli₁
 
 /-- Second version, with pointwise equicontinuity and range in a compact subset -/
@@ -894,7 +887,6 @@ theorem norm_coe_le_norm (x : α) : ‖f x‖ ≤ ‖f‖ :=
   calc
     ‖f x‖ = dist (f x) ((0 : α →ᵇ β) x) := by simp [dist_zero_right]
     _ ≤ ‖f‖ := dist_coe_le_dist _
-    
 #align bounded_continuous_function.norm_coe_le_norm BoundedContinuousFunction.norm_coe_le_norm
 
 theorem dist_le_two_norm' {f : γ → β} {C : ℝ} (hC : ∀ x, ‖f x‖ ≤ C) (x y : γ) :
@@ -903,7 +895,6 @@ theorem dist_le_two_norm' {f : γ → β} {C : ℝ} (hC : ∀ x, ‖f x‖ ≤ C
     dist (f x) (f y) ≤ ‖f x‖ + ‖f y‖ := dist_le_norm_add_norm _ _
     _ ≤ C + C := (add_le_add (hC x) (hC y))
     _ = 2 * C := (two_mul _).symm
-    
 #align bounded_continuous_function.dist_le_two_norm' BoundedContinuousFunction.dist_le_two_norm'
 
 /-- Distance between the images of any two points is at most twice the norm of the function. -/
@@ -1508,8 +1499,7 @@ instance hasSmul' : SMul (α →ᵇ 𝕜) (α →ᵇ β) :=
       calc
         ‖f x • g x‖ ≤ ‖f x‖ * ‖g x‖ := norm_smul_le _ _
         _ ≤ ‖f‖ * ‖g‖ :=
-          mul_le_mul (f.norm_coe_le_norm _) (g.norm_coe_le_norm _) (norm_nonneg _) (norm_nonneg _)
-        ⟩
+          mul_le_mul (f.norm_coe_le_norm _) (g.norm_coe_le_norm _) (norm_nonneg _) (norm_nonneg _)⟩
 #align bounded_continuous_function.has_smul' BoundedContinuousFunction.hasSmul'
 -/
 

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

@@ -563,7 +563,7 @@ variable [TopologicalSpace α] [CompactSpace α] [PseudoMetricSpace β]
 
 variable {f g : α →ᵇ β} {x : α} {C : ℝ}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y z «expr ∈ » U) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (y z «expr ∈ » U) -/
 /- Arzela-Ascoli theorem asserts that, on a compact space, a set of functions sharing
 a common modulus of continuity and taking values in a compact set forms a compact
 subset for the topology of uniform convergence. In this section, we prove this theorem

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

@@ -170,9 +170,9 @@ def mkOfDiscrete [DiscreteTopology α] (f : α → β) (C : ℝ) (h : ∀ x y :
 
 /-- The uniform distance between two bounded continuous functions -/
 instance : Dist (α →ᵇ β) :=
-  ⟨fun f g => sInf { C | 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C }⟩
+  ⟨fun f g => sInf {C | 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C}⟩
 
-theorem dist_eq : dist f g = sInf { C | 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C } :=
+theorem dist_eq : dist f g = sInf {C | 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C} :=
   rfl
 #align bounded_continuous_function.dist_eq BoundedContinuousFunction.dist_eq
 
@@ -249,7 +249,7 @@ instance {α β} [TopologicalSpace α] [MetricSpace β] : MetricSpace (α →ᵇ
     where eq_of_dist_eq_zero f g hfg := by
     ext x <;> exact eq_of_dist_eq_zero (le_antisymm (hfg ▸ dist_coe_le_dist _) dist_nonneg)
 
-theorem nndist_eq : nndist f g = sInf { C | ∀ x : α, nndist (f x) (g x) ≤ C } :=
+theorem nndist_eq : nndist f g = sInf {C | ∀ x : α, nndist (f x) (g x) ≤ C} :=
   Subtype.ext <|
     dist_eq.trans <| by
       rw [NNReal.coe_sInf, NNReal.coe_image]
@@ -869,13 +869,13 @@ theorem norm_def : ‖f‖ = dist f 0 :=
 
 /-- The norm of a bounded continuous function is the supremum of `‖f x‖`.
 We use `Inf` to ensure that the definition works if `α` has no elements. -/
-theorem norm_eq (f : α →ᵇ β) : ‖f‖ = sInf { C : ℝ | 0 ≤ C ∧ ∀ x : α, ‖f x‖ ≤ C } := by
+theorem norm_eq (f : α →ᵇ β) : ‖f‖ = sInf {C : ℝ | 0 ≤ C ∧ ∀ x : α, ‖f x‖ ≤ C} := by
   simp [norm_def, BoundedContinuousFunction.dist_eq]
 #align bounded_continuous_function.norm_eq BoundedContinuousFunction.norm_eq
 
 /-- When the domain is non-empty, we do not need the `0 ≤ C` condition in the formula for ‖f‖ as an
 `Inf`. -/
-theorem norm_eq_of_nonempty [h : Nonempty α] : ‖f‖ = sInf { C : ℝ | ∀ x : α, ‖f x‖ ≤ C } :=
+theorem norm_eq_of_nonempty [h : Nonempty α] : ‖f‖ = sInf {C : ℝ | ∀ x : α, ‖f x‖ ≤ C} :=
   by
   obtain ⟨a⟩ := h
   rw [norm_eq]

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

@@ -46,7 +46,7 @@ you should parametrize over `(F : Type*) [bounded_continuous_map_class F α β]
 
 When you extend this structure, make sure to extend `bounded_continuous_map_class`. -/
 structure BoundedContinuousFunction (α : Type u) (β : Type v) [TopologicalSpace α]
-  [PseudoMetricSpace β] extends ContinuousMap α β : Type max u v where
+    [PseudoMetricSpace β] extends ContinuousMap α β : Type max u v where
   map_bounded' : ∃ C, ∀ x y, dist (to_fun x) (to_fun y) ≤ C
 #align bounded_continuous_function BoundedContinuousFunction
 -/
@@ -61,7 +61,7 @@ section
 
 You should also extend this typeclass when you extend `bounded_continuous_function`. -/
 class BoundedContinuousMapClass (F α β : Type _) [TopologicalSpace α] [PseudoMetricSpace β] extends
-  ContinuousMapClass F α β where
+    ContinuousMapClass F α β where
   map_bounded (f : F) : ∃ C, ∀ x y, dist (f x) (f y) ≤ C
 #align bounded_continuous_map_class BoundedContinuousMapClass
 -/
@@ -179,8 +179,8 @@ theorem dist_eq : dist f g = sInf { C | 0 ≤ C ∧ ∀ x : α, dist (f x) (g x)
 theorem dist_set_exists : ∃ C, 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C :=
   by
   rcases f.bounded_range.union g.bounded_range with ⟨C, hC⟩
-  refine' ⟨max 0 C, le_max_left _ _, fun x => (hC _ _ _ _).trans (le_max_right _ _)⟩ <;>
-      [left;right] <;>
+  refine' ⟨max 0 C, le_max_left _ _, fun x => (hC _ _ _ _).trans (le_max_right _ _)⟩ <;> [left;
+      right] <;>
     apply mem_range_self
 #align bounded_continuous_function.dist_set_exists BoundedContinuousFunction.dist_set_exists
 
@@ -572,7 +572,7 @@ and several useful variations around it. -/
 theorem arzela_ascoli₁ [CompactSpace β] (A : Set (α →ᵇ β)) (closed : IsClosed A)
     (H : Equicontinuous (coeFn : A → α → β)) : IsCompact A :=
   by
-  simp_rw [Equicontinuous, Metric.equicontinuousAt_iff_pair] at H
+  simp_rw [Equicontinuous, Metric.equicontinuousAt_iff_pair] at H 
   refine' isCompact_of_totallyBounded_isClosed _ closed
   refine' totally_bounded_of_finite_discretization fun ε ε0 => _
   rcases exists_between ε0 with ⟨ε₁, ε₁0, εε₁⟩
@@ -652,7 +652,7 @@ theorem arzela_ascoli₂ (s : Set β) (hs : IsCompact s) (A : Set (α →ᵇ β)
     rw [uniform_embedding_subtype_coe.to_uniform_inducing.equicontinuous_iff]
     exact H.comp (A.restrict_preimage F)
   · let g := cod_restrict s f fun x => in_s f x hf
-    rw [show f = F g by ext <;> rfl] at hf⊢
+    rw [show f = F g by ext <;> rfl] at hf ⊢
     exact ⟨g, hf, rfl⟩
 #align bounded_continuous_function.arzela_ascoli₂ BoundedContinuousFunction.arzela_ascoli₂
 
@@ -824,7 +824,7 @@ def toContinuousMapAddHom : (α →ᵇ β) →+ C(α, β)
     where
   toFun := toContinuousMap
   map_zero' := by ext; simp
-  map_add' := by intros ; ext; simp
+  map_add' := by intros; ext; simp
 #align bounded_continuous_function.to_continuous_map_add_hom BoundedContinuousFunction.toContinuousMapAddHom
 
 end LipschitzAdd
@@ -1535,8 +1535,8 @@ theorem Nnreal.upper_bound {α : Type _} [TopologicalSpace α] (f : α →ᵇ 
     f x ≤ nndist f 0 :=
   by
   have key : nndist (f x) ((0 : α →ᵇ ℝ≥0) x) ≤ nndist f 0 := @dist_coe_le_dist α ℝ≥0 _ _ f 0 x
-  simp only [coe_zero, Pi.zero_apply] at key
-  rwa [NNReal.nndist_zero_eq_val' (f x)] at key
+  simp only [coe_zero, Pi.zero_apply] at key 
+  rwa [NNReal.nndist_zero_eq_val' (f x)] at key 
 #align bounded_continuous_function.nnreal.upper_bound BoundedContinuousFunction.Nnreal.upper_bound
 
 /-!
@@ -1638,7 +1638,7 @@ instance : SemilatticeInf (α →ᵇ β) :=
           obtain ⟨C₁, hf⟩ := f.bounded
           obtain ⟨C₂, hg⟩ := g.bounded
           refine' ⟨C₁ + C₂, fun x y => _⟩
-          simp_rw [NormedAddCommGroup.dist_eq] at hf hg⊢
+          simp_rw [NormedAddCommGroup.dist_eq] at hf hg ⊢
           exact (norm_inf_sub_inf_le_add_norm _ _ _ _).trans (add_le_add (hf _ _) (hg _ _)) }
     inf_le_left := fun f g => ContinuousMap.le_def.mpr fun _ => inf_le_left
     inf_le_right := fun f g => ContinuousMap.le_def.mpr fun _ => inf_le_right
@@ -1656,7 +1656,7 @@ instance : SemilatticeSup (α →ᵇ β) :=
           obtain ⟨C₁, hf⟩ := f.bounded
           obtain ⟨C₂, hg⟩ := g.bounded
           refine' ⟨C₁ + C₂, fun x y => _⟩
-          simp_rw [NormedAddCommGroup.dist_eq] at hf hg⊢
+          simp_rw [NormedAddCommGroup.dist_eq] at hf hg ⊢
           exact (norm_sup_sub_sup_le_add_norm _ _ _ _).trans (add_le_add (hf _ _) (hg _ _)) }
     le_sup_left := fun f g => ContinuousMap.le_def.mpr fun _ => le_sup_left
     le_sup_right := fun f g => ContinuousMap.le_def.mpr fun _ => le_sup_right

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

@@ -29,7 +29,7 @@ the uniform distance.
 
 noncomputable section
 
-open Topology Classical NNReal uniformity UniformConvergence
+open scoped Topology Classical NNReal uniformity UniformConvergence
 
 open Set Filter Metric Function
 
@@ -837,7 +837,7 @@ variable [TopologicalSpace α] [PseudoMetricSpace β] [AddCommMonoid β] [Lipsch
 instance : AddCommMonoid (α →ᵇ β) :=
   { BoundedContinuousFunction.addMonoid with add_comm := fun f g => by ext <;> simp [add_comm] }
 
-open BigOperators
+open scoped BigOperators
 
 @[simp]
 theorem coe_sum {ι : Type _} (s : Finset ι) (f : ι → α →ᵇ β) :
@@ -1110,9 +1110,11 @@ theorem nnnorm_le (C : ℝ≥0) : ‖f‖₊ ≤ C ↔ ∀ x : α, ‖f x‖₊
   norm_le C.Prop
 #align bounded_continuous_function.nnnorm_le BoundedContinuousFunction.nnnorm_le
 
+#print BoundedContinuousFunction.nnnorm_const_le /-
 theorem nnnorm_const_le (b : β) : ‖const α b‖₊ ≤ ‖b‖₊ :=
   norm_const_le _
 #align bounded_continuous_function.nnnorm_const_le BoundedContinuousFunction.nnnorm_const_le
+-/
 
 #print BoundedContinuousFunction.nnnorm_const_eq /-
 @[simp]

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

@@ -96,12 +96,6 @@ instance [BoundedContinuousMapClass F α β] : CoeTC F (α →ᵇ β) :=
       continuous_toFun := map_continuous f
       map_bounded' := map_bounded f }⟩
 
-/- warning: bounded_continuous_function.coe_to_continuous_fun -> BoundedContinuousFunction.coe_to_continuous_fun is a dubious translation:
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 @[simp]
 theorem coe_to_continuous_fun (f : α →ᵇ β) : (f.toContinuousMap : α → β) = f :=
   rfl
@@ -117,53 +111,23 @@ def Simps.apply (h : α →ᵇ β) : α → β :=
 
 initialize_simps_projections BoundedContinuousFunction (to_continuous_map_to_fun → apply)
 
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 protected theorem bounded (f : α →ᵇ β) : ∃ C, ∀ x y : α, dist (f x) (f y) ≤ C :=
   f.map_bounded'
 #align bounded_continuous_function.bounded BoundedContinuousFunction.bounded
 
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 protected theorem continuous (f : α →ᵇ β) : Continuous f :=
   f.toContinuousMap.Continuous
 #align bounded_continuous_function.continuous BoundedContinuousFunction.continuous
 
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 @[ext]
 theorem ext (h : ∀ x, f x = g x) : f = g :=
   FunLike.ext _ _ h
 #align bounded_continuous_function.ext BoundedContinuousFunction.ext
 
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 theorem bounded_range (f : α →ᵇ β) : Bounded (range f) :=
   bounded_range_iff.2 f.Bounded
 #align bounded_continuous_function.bounded_range BoundedContinuousFunction.bounded_range
 
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 theorem bounded_image (f : α →ᵇ β) (s : Set α) : Bounded (f '' s) :=
   f.bounded_range.mono <| image_subset_range _ _
 #align bounded_continuous_function.bounded_image BoundedContinuousFunction.bounded_image
@@ -174,23 +138,11 @@ theorem eq_of_empty [IsEmpty α] (f g : α →ᵇ β) : f = g :=
 #align bounded_continuous_function.eq_of_empty BoundedContinuousFunction.eq_of_empty
 -/
 
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 /-- A continuous function with an explicit bound is a bounded continuous function. -/
 def mkOfBound (f : C(α, β)) (C : ℝ) (h : ∀ x y : α, dist (f x) (f y) ≤ C) : α →ᵇ β :=
   ⟨f, ⟨C, h⟩⟩
 #align bounded_continuous_function.mk_of_bound BoundedContinuousFunction.mkOfBound
 
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 @[simp]
 theorem mkOfBound_coe {f} {C} {h} : (mkOfBound f C h : α → β) = (f : α → β) :=
   rfl
@@ -203,23 +155,11 @@ def mkOfCompact [CompactSpace α] (f : C(α, β)) : α →ᵇ β :=
 #align bounded_continuous_function.mk_of_compact BoundedContinuousFunction.mkOfCompact
 -/
 
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 @[simp]
 theorem mkOfCompact_apply [CompactSpace α] (f : C(α, β)) (a : α) : mkOfCompact f a = f a :=
   rfl
 #align bounded_continuous_function.mk_of_compact_apply BoundedContinuousFunction.mkOfCompact_apply
 
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 /-- If a function is bounded on a discrete space, it is automatically continuous,
 and therefore gives rise to an element of the type of bounded continuous functions -/
 @[simps]
@@ -232,22 +172,10 @@ def mkOfDiscrete [DiscreteTopology α] (f : α → β) (C : ℝ) (h : ∀ x y :
 instance : Dist (α →ᵇ β) :=
   ⟨fun f g => sInf { C | 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C }⟩
 
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 theorem dist_eq : dist f g = sInf { C | 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C } :=
   rfl
 #align bounded_continuous_function.dist_eq BoundedContinuousFunction.dist_eq
 
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 theorem dist_set_exists : ∃ C, 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C :=
   by
   rcases f.bounded_range.union g.bounded_range with ⟨C, hC⟩
@@ -256,12 +184,6 @@ theorem dist_set_exists : ∃ C, 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C
     apply mem_range_self
 #align bounded_continuous_function.dist_set_exists BoundedContinuousFunction.dist_set_exists
 
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 /-- The pointwise distance is controlled by the distance between functions, by definition. -/
 theorem dist_coe_le_dist (x : α) : dist (f x) (g x) ≤ dist f g :=
   le_csInf dist_set_exists fun b hb => hb.2 x
@@ -273,34 +195,16 @@ in metric spaces. -/
 private theorem dist_nonneg' : 0 ≤ dist f g :=
   le_csInf dist_set_exists fun C => And.left
 
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 /-- The distance between two functions is controlled by the supremum of the pointwise distances -/
 theorem dist_le (C0 : (0 : ℝ) ≤ C) : dist f g ≤ C ↔ ∀ x : α, dist (f x) (g x) ≤ C :=
   ⟨fun h x => le_trans (dist_coe_le_dist x) h, fun H => csInf_le ⟨0, fun C => And.left⟩ ⟨C0, H⟩⟩
 #align bounded_continuous_function.dist_le BoundedContinuousFunction.dist_le
 
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 theorem dist_le_iff_of_nonempty [Nonempty α] : dist f g ≤ C ↔ ∀ x, dist (f x) (g x) ≤ C :=
   ⟨fun h x => le_trans (dist_coe_le_dist x) h, fun w =>
     (dist_le (le_trans dist_nonneg (w (Nonempty.some ‹_›)))).mpr w⟩
 #align bounded_continuous_function.dist_le_iff_of_nonempty BoundedContinuousFunction.dist_le_iff_of_nonempty
 
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 theorem dist_lt_of_nonempty_compact [Nonempty α] [CompactSpace α]
     (w : ∀ x : α, dist (f x) (g x) < C) : dist f g < C :=
   by
@@ -310,12 +214,6 @@ theorem dist_lt_of_nonempty_compact [Nonempty α] [CompactSpace α]
   exact lt_of_le_of_lt (dist_le_iff_of_nonempty.mpr fun y => le y trivial) (w x)
 #align bounded_continuous_function.dist_lt_of_nonempty_compact BoundedContinuousFunction.dist_lt_of_nonempty_compact
 
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 theorem dist_lt_iff_of_compact [CompactSpace α] (C0 : (0 : ℝ) < C) :
     dist f g < C ↔ ∀ x : α, dist (f x) (g x) < C :=
   by
@@ -332,12 +230,6 @@ theorem dist_lt_iff_of_compact [CompactSpace α] (C0 : (0 : ℝ) < C) :
       exact csInf_le ⟨0, fun C => And.left⟩ ⟨le_rfl, fun x => False.elim (h (Nonempty.intro x))⟩
 #align bounded_continuous_function.dist_lt_iff_of_compact BoundedContinuousFunction.dist_lt_iff_of_compact
 
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 theorem dist_lt_iff_of_nonempty_compact [Nonempty α] [CompactSpace α] :
     dist f g < C ↔ ∀ x : α, dist (f x) (g x) < C :=
   ⟨fun w x => lt_of_le_of_lt (dist_coe_le_dist x) w, dist_lt_of_nonempty_compact⟩
@@ -357,12 +249,6 @@ instance {α β} [TopologicalSpace α] [MetricSpace β] : MetricSpace (α →ᵇ
     where eq_of_dist_eq_zero f g hfg := by
     ext x <;> exact eq_of_dist_eq_zero (le_antisymm (hfg ▸ dist_coe_le_dist _) dist_nonneg)
 
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 theorem nndist_eq : nndist f g = sInf { C | ∀ x : α, nndist (f x) (g x) ≤ C } :=
   Subtype.ext <|
     dist_eq.trans <| by
@@ -370,43 +256,19 @@ theorem nndist_eq : nndist f g = sInf { C | ∀ x : α, nndist (f x) (g x) ≤ C
       simp_rw [mem_set_of_eq, ← NNReal.coe_le_coe, Subtype.coe_mk, exists_prop, coe_nndist]
 #align bounded_continuous_function.nndist_eq BoundedContinuousFunction.nndist_eq
 
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 theorem nndist_set_exists : ∃ C, ∀ x : α, nndist (f x) (g x) ≤ C :=
   Subtype.exists.mpr <| dist_set_exists.imp fun a ⟨ha, h⟩ => ⟨ha, h⟩
 #align bounded_continuous_function.nndist_set_exists BoundedContinuousFunction.nndist_set_exists
 
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 theorem nndist_coe_le_nndist (x : α) : nndist (f x) (g x) ≤ nndist f g :=
   dist_coe_le_dist x
 #align bounded_continuous_function.nndist_coe_le_nndist BoundedContinuousFunction.nndist_coe_le_nndist
 
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 /-- On an empty space, bounded continuous functions are at distance 0 -/
 theorem dist_zero_of_empty [IsEmpty α] : dist f g = 0 := by
   rw [(ext isEmptyElim : f = g), dist_self]
 #align bounded_continuous_function.dist_zero_of_empty BoundedContinuousFunction.dist_zero_of_empty
 
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 theorem dist_eq_iSup : dist f g = ⨆ x : α, dist (f x) (g x) :=
   by
   cases isEmpty_or_nonempty α; · rw [iSup_of_empty', Real.sSup_empty, dist_zero_of_empty]
@@ -414,22 +276,10 @@ theorem dist_eq_iSup : dist f g = ⨆ x : α, dist (f x) (g x) :=
   exact dist_set_exists.imp fun C hC => forall_range_iff.2 hC.2
 #align bounded_continuous_function.dist_eq_supr BoundedContinuousFunction.dist_eq_iSup
 
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 theorem nndist_eq_iSup : nndist f g = ⨆ x : α, nndist (f x) (g x) :=
   Subtype.ext <| dist_eq_iSup.trans <| by simp_rw [NNReal.coe_iSup, coe_nndist]
 #align bounded_continuous_function.nndist_eq_supr BoundedContinuousFunction.nndist_eq_iSup
 
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 theorem tendsto_iff_tendstoUniformly {ι : Type _} {F : ι → α →ᵇ β} {f : α →ᵇ β} {l : Filter ι} :
     Tendsto F l (𝓝 f) ↔ TendstoUniformly (fun i => F i) f l :=
   Iff.intro
@@ -447,12 +297,6 @@ theorem tendsto_iff_tendstoUniformly {ι : Type _} {F : ι → α →ᵇ β} {f
             (half_lt_self ε_pos))
 #align bounded_continuous_function.tendsto_iff_tendsto_uniformly BoundedContinuousFunction.tendsto_iff_tendstoUniformly
 
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 /-- The topology on `α →ᵇ β` is exactly the topology induced by the natural map to `α →ᵤ β`. -/
 theorem inducing_coeFn : Inducing (UniformFun.ofFun ∘ coeFn : (α →ᵇ β) → α →ᵤ β) :=
   by
@@ -463,12 +307,6 @@ theorem inducing_coeFn : Inducing (UniformFun.ofFun ∘ coeFn : (α →ᵇ β) 
   rfl
 #align bounded_continuous_function.inducing_coe_fn BoundedContinuousFunction.inducing_coeFn
 
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 -- TODO: upgrade to a `uniform_embedding`
 theorem embedding_coeFn : Embedding (UniformFun.ofFun ∘ coeFn : (α →ᵇ β) → α →ᵤ β) :=
   ⟨inducing_coeFn, fun f g h => ext fun x => congr_fun h x⟩
@@ -486,12 +324,6 @@ def const (b : β) : α →ᵇ β :=
 
 variable {α}
 
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 theorem const_apply' (a : α) (b : β) : (const α b : α → β) a = b :=
   rfl
 #align bounded_continuous_function.const_apply' BoundedContinuousFunction.const_apply'
@@ -500,54 +332,24 @@ theorem const_apply' (a : α) (b : β) : (const α b : α → β) a = b :=
 instance [Inhabited β] : Inhabited (α →ᵇ β) :=
   ⟨const α default⟩
 
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 theorem lipschitz_evalx (x : α) : LipschitzWith 1 fun f : α →ᵇ β => f x :=
   LipschitzWith.mk_one fun f g => dist_coe_le_dist x
 #align bounded_continuous_function.lipschitz_evalx BoundedContinuousFunction.lipschitz_evalx
 
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 theorem uniformContinuous_coe : @UniformContinuous (α →ᵇ β) (α → β) _ _ coeFn :=
   uniformContinuous_pi.2 fun x => (lipschitz_evalx x).UniformContinuous
 #align bounded_continuous_function.uniform_continuous_coe BoundedContinuousFunction.uniformContinuous_coe
 
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 theorem continuous_coe : Continuous fun (f : α →ᵇ β) x => f x :=
   UniformContinuous.continuous uniformContinuous_coe
 #align bounded_continuous_function.continuous_coe BoundedContinuousFunction.continuous_coe
 
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 /-- When `x` is fixed, `(f : α →ᵇ β) ↦ f x` is continuous -/
 @[continuity]
 theorem continuous_eval_const {x : α} : Continuous fun f : α →ᵇ β => f x :=
   (continuous_apply x).comp continuous_coe
 #align bounded_continuous_function.continuous_eval_const BoundedContinuousFunction.continuous_eval_const
 
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 /-- The evaluation map is continuous, as a joint function of `u` and `x` -/
 @[continuity]
 theorem continuous_eval : Continuous fun p : (α →ᵇ β) × α => p.1 p.2 :=
@@ -601,47 +403,23 @@ def compContinuous {δ : Type _} [TopologicalSpace δ] (f : α →ᵇ β) (g : C
 #align bounded_continuous_function.comp_continuous BoundedContinuousFunction.compContinuous
 -/
 
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 @[simp]
 theorem coe_compContinuous {δ : Type _} [TopologicalSpace δ] (f : α →ᵇ β) (g : C(δ, α)) :
     coeFn (f.comp_continuous g) = f ∘ g :=
   rfl
 #align bounded_continuous_function.coe_comp_continuous BoundedContinuousFunction.coe_compContinuous
 
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 @[simp]
 theorem compContinuous_apply {δ : Type _} [TopologicalSpace δ] (f : α →ᵇ β) (g : C(δ, α)) (x : δ) :
     f.comp_continuous g x = f (g x) :=
   rfl
 #align bounded_continuous_function.comp_continuous_apply BoundedContinuousFunction.compContinuous_apply
 
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 theorem lipschitz_compContinuous {δ : Type _} [TopologicalSpace δ] (g : C(δ, α)) :
     LipschitzWith 1 fun f : α →ᵇ β => f.comp_continuous g :=
   LipschitzWith.mk_one fun f₁ f₂ => (dist_le dist_nonneg).2 fun x => dist_coe_le_dist (g x)
 #align bounded_continuous_function.lipschitz_comp_continuous BoundedContinuousFunction.lipschitz_compContinuous
 
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 theorem continuous_compContinuous {δ : Type _} [TopologicalSpace δ] (g : C(δ, α)) :
     Continuous fun f : α →ᵇ β => f.comp_continuous g :=
   (lipschitz_compContinuous g).Continuous
@@ -654,23 +432,11 @@ def restrict (f : α →ᵇ β) (s : Set α) : s →ᵇ β :=
 #align bounded_continuous_function.restrict BoundedContinuousFunction.restrict
 -/
 
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 @[simp]
 theorem coe_restrict (f : α →ᵇ β) (s : Set α) : coeFn (f.restrict s) = f ∘ coe :=
   rfl
 #align bounded_continuous_function.coe_restrict BoundedContinuousFunction.coe_restrict
 
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 @[simp]
 theorem restrict_apply (f : α →ᵇ β) (s : Set α) (x : s) : f.restrict s x = f x :=
   rfl
@@ -691,12 +457,6 @@ def comp (G : β → γ) {C : ℝ≥0} (H : LipschitzWith C G) (f : α →ᵇ β
 #align bounded_continuous_function.comp BoundedContinuousFunction.comp
 -/
 
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 /-- The composition operator (in the target) with a Lipschitz map is Lipschitz -/
 theorem lipschitz_comp {G : β → γ} {C : ℝ≥0} (H : LipschitzWith C G) :
     LipschitzWith C (comp G H : (α →ᵇ β) → α →ᵇ γ) :=
@@ -708,36 +468,18 @@ theorem lipschitz_comp {G : β → γ} {C : ℝ≥0} (H : LipschitzWith C G) :
         
 #align bounded_continuous_function.lipschitz_comp BoundedContinuousFunction.lipschitz_comp
 
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 /-- The composition operator (in the target) with a Lipschitz map is uniformly continuous -/
 theorem uniformContinuous_comp {G : β → γ} {C : ℝ≥0} (H : LipschitzWith C G) :
     UniformContinuous (comp G H : (α →ᵇ β) → α →ᵇ γ) :=
   (lipschitz_comp H).UniformContinuous
 #align bounded_continuous_function.uniform_continuous_comp BoundedContinuousFunction.uniformContinuous_comp
 
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 /-- The composition operator (in the target) with a Lipschitz map is continuous -/
 theorem continuous_comp {G : β → γ} {C : ℝ≥0} (H : LipschitzWith C G) :
     Continuous (comp G H : (α →ᵇ β) → α →ᵇ γ) :=
   (lipschitz_comp H).Continuous
 #align bounded_continuous_function.continuous_comp BoundedContinuousFunction.continuous_comp
 
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 /-- Restriction (in the target) of a bounded continuous function taking values in a subset -/
 def codRestrict (s : Set β) (f : α →ᵇ β) (H : ∀ x, f x ∈ s) : α →ᵇ s :=
   ⟨⟨s.codRestrict f H, f.Continuous.subtype_mk _⟩, f.Bounded⟩
@@ -761,52 +503,25 @@ def extend (f : α ↪ δ) (g : α →ᵇ β) (h : δ →ᵇ β) : δ →ᵇ β
 #align bounded_continuous_function.extend BoundedContinuousFunction.extend
 -/
 
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 @[simp]
 theorem extend_apply (f : α ↪ δ) (g : α →ᵇ β) (h : δ →ᵇ β) (x : α) : extend f g h (f x) = g x :=
   f.Injective.extend_apply _ _ _
 #align bounded_continuous_function.extend_apply BoundedContinuousFunction.extend_apply
 
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 @[simp]
 theorem extend_comp (f : α ↪ δ) (g : α →ᵇ β) (h : δ →ᵇ β) : extend f g h ∘ f = g :=
   extend_comp f.Injective _ _
 #align bounded_continuous_function.extend_comp BoundedContinuousFunction.extend_comp
 
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 theorem extend_apply' {f : α ↪ δ} {x : δ} (hx : x ∉ range f) (g : α →ᵇ β) (h : δ →ᵇ β) :
     extend f g h x = h x :=
   extend_apply' _ _ _ hx
 #align bounded_continuous_function.extend_apply' BoundedContinuousFunction.extend_apply'
 
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 theorem extend_of_empty [IsEmpty α] (f : α ↪ δ) (g : α →ᵇ β) (h : δ →ᵇ β) : extend f g h = h :=
   FunLike.coe_injective <| Function.extend_of_isEmpty f g h
 #align bounded_continuous_function.extend_of_empty BoundedContinuousFunction.extend_of_empty
 
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-<too large>
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 @[simp]
 theorem dist_extend_extend (f : α ↪ δ) (g₁ g₂ : α →ᵇ β) (h₁ h₂ : δ →ᵇ β) :
     dist (g₁.extend f h₁) (g₂.extend f h₂) =
@@ -834,12 +549,6 @@ theorem dist_extend_extend (f : α ↪ δ) (g₁ g₂ : α →ᵇ β) (h₁ h₂
       
 #align bounded_continuous_function.dist_extend_extend BoundedContinuousFunction.dist_extend_extend
 
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 theorem isometry_extend (f : α ↪ δ) (h : δ →ᵇ β) : Isometry fun g : α →ᵇ β => extend f g h :=
   Isometry.of_dist_eq fun g₁ g₂ => by simp [dist_nonneg]
 #align bounded_continuous_function.isometry_extend BoundedContinuousFunction.isometry_extend
@@ -854,12 +563,6 @@ variable [TopologicalSpace α] [CompactSpace α] [PseudoMetricSpace β]
 
 variable {f g : α →ᵇ β} {x : α} {C : ℝ}
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y z «expr ∈ » U) -/
 /- Arzela-Ascoli theorem asserts that, on a compact space, a set of functions sharing
 a common modulus of continuity and taking values in a compact set forms a compact
@@ -932,12 +635,6 @@ theorem arzela_ascoli₁ [CompactSpace β] (A : Set (α →ᵇ β)) (closed : Is
       
 #align bounded_continuous_function.arzela_ascoli₁ BoundedContinuousFunction.arzela_ascoli₁
 
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 /-- Second version, with pointwise equicontinuity and range in a compact subset -/
 theorem arzela_ascoli₂ (s : Set β) (hs : IsCompact s) (A : Set (α →ᵇ β)) (closed : IsClosed A)
     (in_s : ∀ (f : α →ᵇ β) (x : α), f ∈ A → f x ∈ s) (H : Equicontinuous (coeFn : A → α → β)) :
@@ -959,12 +656,6 @@ theorem arzela_ascoli₂ (s : Set β) (hs : IsCompact s) (A : Set (α →ᵇ β)
     exact ⟨g, hf, rfl⟩
 #align bounded_continuous_function.arzela_ascoli₂ BoundedContinuousFunction.arzela_ascoli₂
 
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 /-- Third (main) version, with pointwise equicontinuity and range in a compact subset, but
 without closedness. The closure is then compact -/
 theorem arzela_ascoli [T2Space β] (s : Set β) (hs : IsCompact s) (A : Set (α →ᵇ β))
@@ -991,12 +682,6 @@ variable [TopologicalSpace α] [PseudoMetricSpace β] [One β]
 instance : One (α →ᵇ β) :=
   ⟨const α 1⟩
 
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 @[simp, to_additive]
 theorem coe_one : ((1 : α →ᵇ β) : α → β) = 1 :=
   rfl
@@ -1011,12 +696,6 @@ theorem mkOfCompact_one [CompactSpace α] : mkOfCompact (1 : C(α, β)) = 1 :=
 #align bounded_continuous_function.mk_of_compact_zero BoundedContinuousFunction.mkOfCompact_zero
 -/
 
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 @[to_additive]
 theorem forall_coe_one_iff_one (f : α →ᵇ β) : (∀ x, f x = 1) ↔ f = 1 :=
   (@FunLike.ext_iff _ _ _ _ f 1).symm
@@ -1066,56 +745,26 @@ instance : Add (α →ᵇ β)
         exact Classical.choose_spec f.bounded x y
         exact Classical.choose_spec g.bounded x y)
 
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 @[simp]
 theorem coe_add : ⇑(f + g) = f + g :=
   rfl
 #align bounded_continuous_function.coe_add BoundedContinuousFunction.coe_add
 
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 theorem add_apply : (f + g) x = f x + g x :=
   rfl
 #align bounded_continuous_function.add_apply BoundedContinuousFunction.add_apply
 
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 @[simp]
 theorem mkOfCompact_add [CompactSpace α] (f g : C(α, β)) :
     mkOfCompact (f + g) = mkOfCompact f + mkOfCompact g :=
   rfl
 #align bounded_continuous_function.mk_of_compact_add BoundedContinuousFunction.mkOfCompact_add
 
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 theorem add_compContinuous [TopologicalSpace γ] (h : C(γ, α)) :
     (g + f).comp_continuous h = g.comp_continuous h + f.comp_continuous h :=
   rfl
 #align bounded_continuous_function.add_comp_continuous BoundedContinuousFunction.add_compContinuous
 
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 @[simp]
 theorem coe_nsmulRec : ∀ n, ⇑(nsmulRec n f) = n • f
   | 0 => by rw [nsmulRec, zero_smul, coe_zero]
@@ -1130,23 +779,11 @@ instance hasNatScalar : SMul ℕ (α →ᵇ β)
 #align bounded_continuous_function.has_nat_scalar BoundedContinuousFunction.hasNatScalar
 -/
 
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 @[simp]
 theorem coe_nsmul (r : ℕ) (f : α →ᵇ β) : ⇑(r • f) = r • f :=
   rfl
 #align bounded_continuous_function.coe_nsmul BoundedContinuousFunction.coe_nsmul
 
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 @[simp]
 theorem nsmul_apply (r : ℕ) (f : α →ᵇ β) (v : α) : (r • f) v = r • f v :=
   rfl
@@ -1180,12 +817,6 @@ def coeFnAddHom : (α →ᵇ β) →+ α → β where
 
 variable (α β)
 
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 /-- The additive map forgetting that a bounded continuous function is bounded.
 -/
 @[simps]
@@ -1208,24 +839,12 @@ instance : AddCommMonoid (α →ᵇ β) :=
 
 open BigOperators
 
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 @[simp]
 theorem coe_sum {ι : Type _} (s : Finset ι) (f : ι → α →ᵇ β) :
     ⇑(∑ i in s, f i) = ∑ i in s, (f i : α → β) :=
   (@coeFnAddHom α β _ _ _ _).map_sum f s
 #align bounded_continuous_function.coe_sum BoundedContinuousFunction.coe_sum
 
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 theorem sum_apply {ι : Type _} (s : Finset ι) (f : ι → α →ᵇ β) (a : α) :
     (∑ i in s, f i) a = ∑ i in s, f i a := by simp
 #align bounded_continuous_function.sum_apply BoundedContinuousFunction.sum_apply
@@ -1244,34 +863,16 @@ variable (f g : α →ᵇ β) {x : α} {C : ℝ}
 instance : Norm (α →ᵇ β) :=
   ⟨fun u => dist u 0⟩
 
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 theorem norm_def : ‖f‖ = dist f 0 :=
   rfl
 #align bounded_continuous_function.norm_def BoundedContinuousFunction.norm_def
 
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 /-- The norm of a bounded continuous function is the supremum of `‖f x‖`.
 We use `Inf` to ensure that the definition works if `α` has no elements. -/
 theorem norm_eq (f : α →ᵇ β) : ‖f‖ = sInf { C : ℝ | 0 ≤ C ∧ ∀ x : α, ‖f x‖ ≤ C } := by
   simp [norm_def, BoundedContinuousFunction.dist_eq]
 #align bounded_continuous_function.norm_eq BoundedContinuousFunction.norm_eq
 
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 /-- When the domain is non-empty, we do not need the `0 ≤ C` condition in the formula for ‖f‖ as an
 `Inf`. -/
 theorem norm_eq_of_nonempty [h : Nonempty α] : ‖f‖ = sInf { C : ℝ | ∀ x : α, ‖f x‖ ≤ C } :=
@@ -1284,23 +885,11 @@ theorem norm_eq_of_nonempty [h : Nonempty α] : ‖f‖ = sInf { C : ℝ | ∀ x
   exact fun h' => le_trans (norm_nonneg (f a)) (h' a)
 #align bounded_continuous_function.norm_eq_of_nonempty BoundedContinuousFunction.norm_eq_of_nonempty
 
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 @[simp]
 theorem norm_eq_zero_of_empty [h : IsEmpty α] : ‖f‖ = 0 :=
   dist_zero_of_empty
 #align bounded_continuous_function.norm_eq_zero_of_empty BoundedContinuousFunction.norm_eq_zero_of_empty
 
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 theorem norm_coe_le_norm (x : α) : ‖f x‖ ≤ ‖f‖ :=
   calc
     ‖f x‖ = dist (f x) ((0 : α →ᵇ β) x) := by simp [dist_zero_right]
@@ -1308,12 +897,6 @@ theorem norm_coe_le_norm (x : α) : ‖f x‖ ≤ ‖f‖ :=
     
 #align bounded_continuous_function.norm_coe_le_norm BoundedContinuousFunction.norm_coe_le_norm
 
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 theorem dist_le_two_norm' {f : γ → β} {C : ℝ} (hC : ∀ x, ‖f x‖ ≤ C) (x y : γ) :
     dist (f x) (f y) ≤ 2 * C :=
   calc
@@ -1323,12 +906,6 @@ theorem dist_le_two_norm' {f : γ → β} {C : ℝ} (hC : ∀ x, ‖f x‖ ≤ C
     
 #align bounded_continuous_function.dist_le_two_norm' BoundedContinuousFunction.dist_le_two_norm'
 
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 /-- Distance between the images of any two points is at most twice the norm of the function. -/
 theorem dist_le_two_norm (x y : α) : dist (f x) (f y) ≤ 2 * ‖f‖ :=
   dist_le_two_norm' f.norm_coe_le_norm x y
@@ -1336,35 +913,17 @@ theorem dist_le_two_norm (x y : α) : dist (f x) (f y) ≤ 2 * ‖f‖ :=
 
 variable {f}
 
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 /-- The norm of a function is controlled by the supremum of the pointwise norms -/
 theorem norm_le (C0 : (0 : ℝ) ≤ C) : ‖f‖ ≤ C ↔ ∀ x : α, ‖f x‖ ≤ C := by
   simpa using @dist_le _ _ _ _ f 0 _ C0
 #align bounded_continuous_function.norm_le BoundedContinuousFunction.norm_le
 
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 theorem norm_le_of_nonempty [Nonempty α] {f : α →ᵇ β} {M : ℝ} : ‖f‖ ≤ M ↔ ∀ x, ‖f x‖ ≤ M :=
   by
   simp_rw [norm_def, ← dist_zero_right]
   exact dist_le_iff_of_nonempty
 #align bounded_continuous_function.norm_le_of_nonempty BoundedContinuousFunction.norm_le_of_nonempty
 
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 theorem norm_lt_iff_of_compact [CompactSpace α] {f : α →ᵇ β} {M : ℝ} (M0 : 0 < M) :
     ‖f‖ < M ↔ ∀ x, ‖f x‖ < M :=
   by
@@ -1372,12 +931,6 @@ theorem norm_lt_iff_of_compact [CompactSpace α] {f : α →ᵇ β} {M : ℝ} (M
   exact dist_lt_iff_of_compact M0
 #align bounded_continuous_function.norm_lt_iff_of_compact BoundedContinuousFunction.norm_lt_iff_of_compact
 
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 theorem norm_lt_iff_of_nonempty_compact [Nonempty α] [CompactSpace α] {f : α →ᵇ β} {M : ℝ} :
     ‖f‖ < M ↔ ∀ x, ‖f x‖ < M :=
   by
@@ -1387,35 +940,17 @@ theorem norm_lt_iff_of_nonempty_compact [Nonempty α] [CompactSpace α] {f : α
 
 variable (f)
 
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 /-- Norm of `const α b` is less than or equal to `‖b‖`. If `α` is nonempty,
 then it is equal to `‖b‖`. -/
 theorem norm_const_le (b : β) : ‖const α b‖ ≤ ‖b‖ :=
   (norm_le (norm_nonneg b)).2 fun x => le_rfl
 #align bounded_continuous_function.norm_const_le BoundedContinuousFunction.norm_const_le
 
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 @[simp]
 theorem norm_const_eq [h : Nonempty α] (b : β) : ‖const α b‖ = ‖b‖ :=
   le_antisymm (norm_const_le b) <| h.elim fun x => (const α b).norm_coe_le_norm x
 #align bounded_continuous_function.norm_const_eq BoundedContinuousFunction.norm_const_eq
 
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 /-- Constructing a bounded continuous function from a uniformly bounded continuous
 function taking values in a normed group. -/
 def ofNormedAddCommGroup {α : Type u} {β : Type v} [TopologicalSpace α] [SeminormedAddCommGroup β]
@@ -1423,12 +958,6 @@ def ofNormedAddCommGroup {α : Type u} {β : Type v} [TopologicalSpace α] [Semi
   ⟨⟨fun n => f n, Hf⟩, ⟨_, dist_le_two_norm' H⟩⟩
 #align bounded_continuous_function.of_normed_add_comm_group BoundedContinuousFunction.ofNormedAddCommGroup
 
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 @[simp]
 theorem coe_ofNormedAddCommGroup {α : Type u} {β : Type v} [TopologicalSpace α]
     [SeminormedAddCommGroup β] (f : α → β) (Hf : Continuous f) (C : ℝ) (H : ∀ x, ‖f x‖ ≤ C) :
@@ -1436,23 +965,11 @@ theorem coe_ofNormedAddCommGroup {α : Type u} {β : Type v} [TopologicalSpace 
   rfl
 #align bounded_continuous_function.coe_of_normed_add_comm_group BoundedContinuousFunction.coe_ofNormedAddCommGroup
 
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 theorem norm_ofNormedAddCommGroup_le {f : α → β} (hfc : Continuous f) {C : ℝ} (hC : 0 ≤ C)
     (hfC : ∀ x, ‖f x‖ ≤ C) : ‖ofNormedAddCommGroup f hfc C hfC‖ ≤ C :=
   (norm_le hC).2 hfC
 #align bounded_continuous_function.norm_of_normed_add_comm_group_le BoundedContinuousFunction.norm_ofNormedAddCommGroup_le
 
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 /-- Constructing a bounded continuous function from a uniformly bounded
 function on a discrete space, taking values in a normed group -/
 def ofNormedAddCommGroupDiscrete {α : Type u} {β : Type v} [TopologicalSpace α] [DiscreteTopology α]
@@ -1460,12 +977,6 @@ def ofNormedAddCommGroupDiscrete {α : Type u} {β : Type v} [TopologicalSpace 
   ofNormedAddCommGroup f continuous_of_discreteTopology C H
 #align bounded_continuous_function.of_normed_add_comm_group_discrete BoundedContinuousFunction.ofNormedAddCommGroupDiscrete
 
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 @[simp]
 theorem coe_ofNormedAddCommGroupDiscrete {α : Type u} {β : Type v} [TopologicalSpace α]
     [DiscreteTopology α] [SeminormedAddCommGroup β] (f : α → β) (C : ℝ) (H : ∀ x, ‖f x‖ ≤ C) :
@@ -1481,43 +992,19 @@ def normComp : α →ᵇ ℝ :=
 #align bounded_continuous_function.norm_comp BoundedContinuousFunction.normComp
 -/
 
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 @[simp]
 theorem coe_normComp : (f.normComp : α → ℝ) = norm ∘ f :=
   rfl
 #align bounded_continuous_function.coe_norm_comp BoundedContinuousFunction.coe_normComp
 
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 @[simp]
 theorem norm_normComp : ‖f.normComp‖ = ‖f‖ := by simp only [norm_eq, coe_norm_comp, norm_norm]
 #align bounded_continuous_function.norm_norm_comp BoundedContinuousFunction.norm_normComp
 
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 theorem bddAbove_range_norm_comp : BddAbove <| Set.range <| norm ∘ f :=
   (Real.bounded_iff_bddBelow_bddAbove.mp <| @bounded_range _ _ _ _ f.normComp).2
 #align bounded_continuous_function.bdd_above_range_norm_comp BoundedContinuousFunction.bddAbove_range_norm_comp
 
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 theorem norm_eq_iSup_norm : ‖f‖ = ⨆ x : α, ‖f x‖ := by
   simp_rw [norm_def, dist_eq_supr, coe_zero, Pi.zero_apply, dist_zero_right]
 #align bounded_continuous_function.norm_eq_supr_norm BoundedContinuousFunction.norm_eq_iSup_norm
@@ -1543,77 +1030,35 @@ instance : Sub (α →ᵇ β) :=
           (add_le_add (f.norm_coe_le_norm x) <|
             trans_rel_right _ (norm_neg _) (g.norm_coe_le_norm x))⟩
 
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 @[simp]
 theorem coe_neg : ⇑(-f) = -f :=
   rfl
 #align bounded_continuous_function.coe_neg BoundedContinuousFunction.coe_neg
 
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 theorem neg_apply : (-f) x = -f x :=
   rfl
 #align bounded_continuous_function.neg_apply BoundedContinuousFunction.neg_apply
 
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 @[simp]
 theorem coe_sub : ⇑(f - g) = f - g :=
   rfl
 #align bounded_continuous_function.coe_sub BoundedContinuousFunction.coe_sub
 
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 theorem sub_apply : (f - g) x = f x - g x :=
   rfl
 #align bounded_continuous_function.sub_apply BoundedContinuousFunction.sub_apply
 
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 @[simp]
 theorem mkOfCompact_neg [CompactSpace α] (f : C(α, β)) : mkOfCompact (-f) = -mkOfCompact f :=
   rfl
 #align bounded_continuous_function.mk_of_compact_neg BoundedContinuousFunction.mkOfCompact_neg
 
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 @[simp]
 theorem mkOfCompact_sub [CompactSpace α] (f g : C(α, β)) :
     mkOfCompact (f - g) = mkOfCompact f - mkOfCompact g :=
   rfl
 #align bounded_continuous_function.mk_of_compact_sub BoundedContinuousFunction.mkOfCompact_sub
 
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 @[simp]
 theorem coe_zsmulRec : ∀ z, ⇑(zsmulRec z f) = z • f
   | Int.ofNat n => by rw [zsmulRec, Int.ofNat_eq_coe, coe_nsmul_rec, coe_nat_zsmul]
@@ -1628,23 +1073,11 @@ instance hasIntScalar : SMul ℤ (α →ᵇ β)
 #align bounded_continuous_function.has_int_scalar BoundedContinuousFunction.hasIntScalar
 -/
 
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 @[simp]
 theorem coe_zsmul (r : ℤ) (f : α →ᵇ β) : ⇑(r • f) = r • f :=
   rfl
 #align bounded_continuous_function.coe_zsmul BoundedContinuousFunction.coe_zsmul
 
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 @[simp]
 theorem zsmul_apply (r : ℤ) (f : α →ᵇ β) (v : α) : (r • f) v = r • f v :=
   rfl
@@ -1660,53 +1093,23 @@ instance : SeminormedAddCommGroup (α →ᵇ β)
 instance {α β} [TopologicalSpace α] [NormedAddCommGroup β] : NormedAddCommGroup (α →ᵇ β) :=
   { BoundedContinuousFunction.seminormedAddCommGroup with }
 
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 theorem nnnorm_def : ‖f‖₊ = nndist f 0 :=
   rfl
 #align bounded_continuous_function.nnnorm_def BoundedContinuousFunction.nnnorm_def
 
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 theorem nnnorm_coe_le_nnnorm (x : α) : ‖f x‖₊ ≤ ‖f‖₊ :=
   norm_coe_le_norm _ _
 #align bounded_continuous_function.nnnorm_coe_le_nnnorm BoundedContinuousFunction.nnnorm_coe_le_nnnorm
 
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 theorem nndist_le_two_nnnorm (x y : α) : nndist (f x) (f y) ≤ 2 * ‖f‖₊ :=
   dist_le_two_norm _ _ _
 #align bounded_continuous_function.nndist_le_two_nnnorm BoundedContinuousFunction.nndist_le_two_nnnorm
 
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 /-- The nnnorm of a function is controlled by the supremum of the pointwise nnnorms -/
 theorem nnnorm_le (C : ℝ≥0) : ‖f‖₊ ≤ C ↔ ∀ x : α, ‖f x‖₊ ≤ C :=
   norm_le C.Prop
 #align bounded_continuous_function.nnnorm_le BoundedContinuousFunction.nnnorm_le
 
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 theorem nnnorm_const_le (b : β) : ‖const α b‖₊ ≤ ‖b‖₊ :=
   norm_const_le _
 #align bounded_continuous_function.nnnorm_const_le BoundedContinuousFunction.nnnorm_const_le
@@ -1718,42 +1121,18 @@ theorem nnnorm_const_eq [h : Nonempty α] (b : β) : ‖const α b‖₊ = ‖b
 #align bounded_continuous_function.nnnorm_const_eq BoundedContinuousFunction.nnnorm_const_eq
 -/
 
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 theorem nnnorm_eq_iSup_nnnorm : ‖f‖₊ = ⨆ x : α, ‖f x‖₊ :=
   Subtype.ext <| (norm_eq_iSup_norm f).trans <| by simp_rw [NNReal.coe_iSup, coe_nnnorm]
 #align bounded_continuous_function.nnnorm_eq_supr_nnnorm BoundedContinuousFunction.nnnorm_eq_iSup_nnnorm
 
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 theorem abs_diff_coe_le_dist : ‖f x - g x‖ ≤ dist f g := by rw [dist_eq_norm];
   exact (f - g).norm_coe_le_norm x
 #align bounded_continuous_function.abs_diff_coe_le_dist BoundedContinuousFunction.abs_diff_coe_le_dist
 
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 theorem coe_le_coe_add_dist {f g : α →ᵇ ℝ} : f x ≤ g x + dist f g :=
   sub_le_iff_le_add'.1 <| (abs_le.1 <| @dist_coe_le_dist _ _ _ _ f g x).2
 #align bounded_continuous_function.coe_le_coe_add_dist BoundedContinuousFunction.coe_le_coe_add_dist
 
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 theorem norm_compContinuous_le [TopologicalSpace γ] (f : α →ᵇ β) (g : C(γ, α)) :
     ‖f.comp_continuous g‖ ≤ ‖f‖ :=
   ((lipschitz_compContinuous g).dist_le_mul f 0).trans <| by
@@ -1791,20 +1170,11 @@ instance : SMul 𝕜 (α →ᵇ β)
           refine' mul_le_mul_of_nonneg_left _ dist_nonneg
           exact hb x y⟩ }
 
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 @[simp]
 theorem coe_smul (c : 𝕜) (f : α →ᵇ β) : ⇑(c • f) = fun x => c • f x :=
   rfl
 #align bounded_continuous_function.coe_smul BoundedContinuousFunction.coe_smul
 
-/- warning: bounded_continuous_function.smul_apply -> BoundedContinuousFunction.smul_apply is a dubious translation:
-<too large>
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 theorem smul_apply (c : 𝕜) (f : α →ᵇ β) (x : α) : (c • f) x = c • f x :=
   rfl
 #align bounded_continuous_function.smul_apply BoundedContinuousFunction.smul_apply
@@ -1863,12 +1233,6 @@ instance : Module 𝕜 (α →ᵇ β) :=
 
 variable (𝕜)
 
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 /-- The evaluation at a point, as a continuous linear map from `α →ᵇ β` to `β`. -/
 def evalClm (x : α) : (α →ᵇ β) →L[𝕜] β where
   toFun f := f x
@@ -1876,9 +1240,6 @@ def evalClm (x : α) : (α →ᵇ β) →L[𝕜] β where
   map_smul' c f := smul_apply _ _ _
 #align bounded_continuous_function.eval_clm BoundedContinuousFunction.evalClm
 
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 @[simp]
 theorem evalClm_apply (x : α) (f : α →ᵇ β) : evalClm 𝕜 x f = f x :=
   rfl
@@ -1886,12 +1247,6 @@ theorem evalClm_apply (x : α) (f : α →ᵇ β) : evalClm 𝕜 x f = f x :=
 
 variable (α β)
 
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-Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.to_continuous_map_linear_map BoundedContinuousFunction.toContinuousMapLinearMapₓ'. -/
 /-- The linear map forgetting that a bounded continuous function is bounded. -/
 @[simps]
 def toContinuousMapLinearMap : (α →ᵇ β) →ₗ[𝕜] C(α, β)
@@ -1935,9 +1290,6 @@ variable [SeminormedAddCommGroup γ] [NormedSpace 𝕜 γ]
 
 variable (α)
 
-/- warning: continuous_linear_map.comp_left_continuous_bounded -> ContinuousLinearMap.compLeftContinuousBounded is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_left_continuous_bounded ContinuousLinearMap.compLeftContinuousBoundedₓ'. -/
 -- TODO does this work in the `has_bounded_smul` setting, too?
 /--
 Postcomposition of bounded continuous functions into a normed module by a continuous linear map is
@@ -1955,9 +1307,6 @@ protected def ContinuousLinearMap.compLeftContinuousBounded (g : β →L[𝕜] 
     norm_ofNormedAddCommGroup_le _ (mul_nonneg (norm_nonneg g) (norm_nonneg f)) _
 #align continuous_linear_map.comp_left_continuous_bounded ContinuousLinearMap.compLeftContinuousBounded
 
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-<too large>
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 @[simp]
 theorem ContinuousLinearMap.compLeftContinuousBounded_apply (g : β →L[𝕜] γ) (f : α →ᵇ β) (x : α) :
     (g.compLeftContinuousBounded α f) x = g (f x) :=
@@ -1990,23 +1339,11 @@ instance : Mul (α →ᵇ R)
       le_trans (norm_mul_le (f x) (g x)) <|
         mul_le_mul (f.norm_coe_le_norm x) (g.norm_coe_le_norm x) (norm_nonneg _) (norm_nonneg _)
 
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 @[simp]
 theorem coe_mul (f g : α →ᵇ R) : ⇑(f * g) = f * g :=
   rfl
 #align bounded_continuous_function.coe_mul BoundedContinuousFunction.coe_mul
 
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 theorem mul_apply (f g : α →ᵇ R) (x : α) : (f * g) x = f x * g x :=
   rfl
 #align bounded_continuous_function.mul_apply BoundedContinuousFunction.mul_apply
@@ -2032,12 +1369,6 @@ section SemiNormed
 
 variable [SeminormedRing R]
 
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 @[simp]
 theorem coe_npowRec (f : α →ᵇ R) : ∀ n, ⇑(npowRec n f) = f ^ n
   | 0 => by rw [npowRec, pow_zero, coe_one]
@@ -2052,23 +1383,11 @@ instance hasNatPow : Pow (α →ᵇ R) ℕ
 #align bounded_continuous_function.has_nat_pow BoundedContinuousFunction.hasNatPow
 -/
 
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 @[simp]
 theorem coe_pow (n : ℕ) (f : α →ᵇ R) : ⇑(f ^ n) = f ^ n :=
   rfl
 #align bounded_continuous_function.coe_pow BoundedContinuousFunction.coe_pow
 
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 @[simp]
 theorem pow_apply (n : ℕ) (f : α →ᵇ R) (v : α) : (f ^ n) v = f v ^ n :=
   rfl
@@ -2077,12 +1396,6 @@ theorem pow_apply (n : ℕ) (f : α →ᵇ R) (v : α) : (f ^ n) v = f v ^ n :=
 instance : NatCast (α →ᵇ R) :=
   ⟨fun n => BoundedContinuousFunction.const _ n⟩
 
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 @[simp, norm_cast]
 theorem coe_natCast (n : ℕ) : ((n : α →ᵇ R) : α → R) = n :=
   rfl
@@ -2091,12 +1404,6 @@ theorem coe_natCast (n : ℕ) : ((n : α →ᵇ R) : α → R) = n :=
 instance : IntCast (α →ᵇ R) :=
   ⟨fun n => BoundedContinuousFunction.const _ n⟩
 
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 @[simp, norm_cast]
 theorem coe_intCast (n : ℤ) : ((n : α →ᵇ R) : α → R) = n :=
   rfl
@@ -2176,9 +1483,6 @@ instance : Algebra 𝕜 (α →ᵇ γ) :=
     commutes' := fun c f => ext fun x => Algebra.commutes' _ _
     smul_def' := fun c f => ext fun x => Algebra.smul_def' _ _ }
 
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 @[simp]
 theorem algebraMap_apply (k : 𝕜) (a : α) : algebraMap 𝕜 (α →ᵇ γ) k a = k • 1 := by
   rw [Algebra.algebraMap_eq_smul_one]; rfl
@@ -2207,12 +1511,6 @@ instance hasSmul' : SMul (α →ᵇ 𝕜) (α →ᵇ β) :=
 #align bounded_continuous_function.has_smul' BoundedContinuousFunction.hasSmul'
 -/
 
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-Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.module' BoundedContinuousFunction.module'ₓ'. -/
 instance module' : Module (α →ᵇ 𝕜) (α →ᵇ β) :=
   Module.ofCore <|
     { smul := (· • ·)
@@ -2222,12 +1520,6 @@ instance module' : Module (α →ᵇ 𝕜) (α →ᵇ β) :=
       one_smul := fun f => ext fun x => one_smul 𝕜 (f x) }
 #align bounded_continuous_function.module' BoundedContinuousFunction.module'
 
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-Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.norm_smul_le BoundedContinuousFunction.norm_smul_leₓ'. -/
 theorem norm_smul_le (f : α →ᵇ 𝕜) (g : α →ᵇ β) : ‖f • g‖ ≤ ‖f‖ * ‖g‖ :=
   norm_ofNormedAddCommGroup_le _ (mul_nonneg (norm_nonneg _) (norm_nonneg _)) _
 #align bounded_continuous_function.norm_smul_le BoundedContinuousFunction.norm_smul_le
@@ -2237,12 +1529,6 @@ show that the space of bounded continuous functions from `α` to `β` is natural
 module over the algebra of bounded continuous functions from `α` to `𝕜`. -/
 end NormedAlgebra
 
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-Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.nnreal.upper_bound BoundedContinuousFunction.Nnreal.upper_boundₓ'. -/
 theorem Nnreal.upper_bound {α : Type _} [TopologicalSpace α] (f : α →ᵇ ℝ≥0) (x : α) :
     f x ≤ nndist f 0 :=
   by
@@ -2282,12 +1568,6 @@ instance : StarAddMonoid (α →ᵇ β)
   star_involutive f := ext fun x => star_star (f x)
   star_add f g := ext fun x => star_add (f x) (g x)
 
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-Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_star BoundedContinuousFunction.coe_starₓ'. -/
 /-- The right-hand side of this equality can be parsed `star ∘ ⇑f` because of the
 instance `pi.has_star`. Upon inspecting the goal, one sees `⊢ ⇑(star f) = star ⇑f`.-/
 @[simp]
@@ -2295,12 +1575,6 @@ theorem coe_star (f : α →ᵇ β) : ⇑(star f) = star f :=
   rfl
 #align bounded_continuous_function.coe_star BoundedContinuousFunction.coe_star
 
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 @[simp]
 theorem star_apply (f : α →ᵇ β) (x : α) : star f x = star (f x) :=
   rfl
@@ -2391,20 +1665,11 @@ instance : SemilatticeSup (α →ᵇ β) :=
 instance : Lattice (α →ᵇ β) :=
   { BoundedContinuousFunction.semilatticeSup, BoundedContinuousFunction.semilatticeInf with }
 
-/- warning: bounded_continuous_function.coe_fn_sup -> BoundedContinuousFunction.coeFn_sup is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_fn_sup BoundedContinuousFunction.coeFn_supₓ'. -/
 @[simp]
 theorem coeFn_sup (f g : α →ᵇ β) : ⇑(f ⊔ g) = f ⊔ g :=
   rfl
 #align bounded_continuous_function.coe_fn_sup BoundedContinuousFunction.coeFn_sup
 
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_inst_2))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2)))) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2)))) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2))))) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2)))) α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2))) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2)))))) f))
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 @[simp]
 theorem coeFn_abs (f : α →ᵇ β) : ⇑(|f|) = |f| :=
   rfl
@@ -2430,35 +1695,17 @@ section NonnegativePart
 
 variable [TopologicalSpace α]
 
-/- warning: bounded_continuous_function.nnreal_part -> BoundedContinuousFunction.nnrealPart is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.nnreal_part BoundedContinuousFunction.nnrealPartₓ'. -/
 /-- The nonnegative part of a bounded continuous `ℝ`-valued function as a bounded
 continuous `ℝ≥0`-valued function. -/
 def nnrealPart (f : α →ᵇ ℝ) : α →ᵇ ℝ≥0 :=
   BoundedContinuousFunction.comp _ (show LipschitzWith 1 Real.toNNReal from lipschitzWith_pos) f
 #align bounded_continuous_function.nnreal_part BoundedContinuousFunction.nnrealPart
 
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 @[simp]
 theorem nnrealPart_coeFn_eq (f : α →ᵇ ℝ) : ⇑f.nnrealPart = Real.toNNReal ∘ ⇑f :=
   rfl
 #align bounded_continuous_function.nnreal_part_coe_fun_eq BoundedContinuousFunction.nnrealPart_coeFn_eq
 
-/- warning: bounded_continuous_function.nnnorm -> BoundedContinuousFunction.nnnorm is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α], (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) -> (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace)
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-Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.nnnorm BoundedContinuousFunction.nnnormₓ'. -/
 /-- The absolute value of a bounded continuous `ℝ`-valued function as a bounded
 continuous `ℝ≥0`-valued function. -/
 def nnnorm (f : α →ᵇ ℝ) : α →ᵇ ℝ≥0 :=
@@ -2466,35 +1713,17 @@ def nnnorm (f : α →ᵇ ℝ) : α →ᵇ ℝ≥0 :=
     (show LipschitzWith 1 fun x : ℝ => ‖x‖₊ from lipschitzWith_one_norm) f
 #align bounded_continuous_function.nnnorm BoundedContinuousFunction.nnnorm
 
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-Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.nnnorm_coe_fun_eq BoundedContinuousFunction.nnnorm_coeFn_eqₓ'. -/
 @[simp]
 theorem nnnorm_coeFn_eq (f : α →ᵇ ℝ) : ⇑f.nnnorm = NNNorm.nnnorm ∘ ⇑f :=
   rfl
 #align bounded_continuous_function.nnnorm_coe_fun_eq BoundedContinuousFunction.nnnorm_coeFn_eq
 
-/- warning: bounded_continuous_function.self_eq_nnreal_part_sub_nnreal_part_neg -> BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_neg is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.self_eq_nnreal_part_sub_nnreal_part_neg BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_negₓ'. -/
 /-- Decompose a bounded continuous function to its positive and negative parts. -/
 theorem self_eq_nnrealPart_sub_nnrealPart_neg (f : α →ᵇ ℝ) :
     ⇑f = coe ∘ f.nnrealPart - coe ∘ (-f).nnrealPart := by funext x; dsimp;
   simp only [max_zero_sub_max_neg_zero_eq_self]
 #align bounded_continuous_function.self_eq_nnreal_part_sub_nnreal_part_neg BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_neg
 
-/- warning: bounded_continuous_function.abs_self_eq_nnreal_part_add_nnreal_part_neg -> BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_neg is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (f : BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace), Eq.{succ u1} (α -> Real) (Function.comp.{succ u1, 1, 1} α Real Real (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) => α -> Real) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) f)) (HAdd.hAdd.{u1, u1, u1} (α -> Real) (α -> Real) (α -> Real) (instHAdd.{u1} (α -> Real) (Pi.instAdd.{u1, 0} α (fun (ᾰ : α) => Real) (fun (i : α) => Real.hasAdd))) (Function.comp.{succ u1, 1, 1} α NNReal Real ((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)))) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) => α -> NNReal) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) (BoundedContinuousFunction.nnrealPart.{u1} α _inst_1 f))) (Function.comp.{succ u1, 1, 1} α NNReal Real ((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)))) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) => α -> NNReal) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) (BoundedContinuousFunction.nnrealPart.{u1} α _inst_1 (Neg.neg.{u1} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) (BoundedContinuousFunction.hasNeg.{u1, 0} α Real _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing))))) f)))))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.abs_self_eq_nnreal_part_add_nnreal_part_neg BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_negₓ'. -/
 /-- Express the absolute value of a bounded continuous function in terms of its
 positive and negative parts. -/
 theorem abs_self_eq_nnrealPart_add_nnrealPart_neg (f : α →ᵇ ℝ) :

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

@@ -81,10 +81,7 @@ variable {f g : α →ᵇ β} {x : α} {C : ℝ}
 instance : BoundedContinuousMapClass (α →ᵇ β) α β
     where
   coe f := f.toFun
-  coe_injective' f g h := by
-    obtain ⟨⟨_, _⟩, _⟩ := f
-    obtain ⟨⟨_, _⟩, _⟩ := g
-    congr
+  coe_injective' f g h := by obtain ⟨⟨_, _⟩, _⟩ := f; obtain ⟨⟨_, _⟩, _⟩ := g; congr
   map_continuous f := f.continuous_toFun
   map_bounded f := f.map_bounded'
 
@@ -1195,13 +1192,8 @@ Case conversion may be inaccurate. Consider using '#align bounded_continuous_fun
 def toContinuousMapAddHom : (α →ᵇ β) →+ C(α, β)
     where
   toFun := toContinuousMap
-  map_zero' := by
-    ext
-    simp
-  map_add' := by
-    intros
-    ext
-    simp
+  map_zero' := by ext; simp
+  map_add' := by intros ; ext; simp
 #align bounded_continuous_function.to_continuous_map_add_hom BoundedContinuousFunction.toContinuousMapAddHom
 
 end LipschitzAdd
@@ -1742,9 +1734,7 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (g : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) {x : α}, LE.le.{0} Real Real.instLEReal (Norm.norm.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (SeminormedAddCommGroup.toNorm.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) _inst_2) (HSub.hSub.{u2, u2, u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (instHSub.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (SubNegMonoid.toSub.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (AddGroup.toSubNegMonoid.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (SeminormedAddGroup.toAddGroup.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) _inst_2))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) g x))) (Dist.dist.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.instDistBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) f g)
 Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.abs_diff_coe_le_dist BoundedContinuousFunction.abs_diff_coe_le_distₓ'. -/
-theorem abs_diff_coe_le_dist : ‖f x - g x‖ ≤ dist f g :=
-  by
-  rw [dist_eq_norm]
+theorem abs_diff_coe_le_dist : ‖f x - g x‖ ≤ dist f g := by rw [dist_eq_norm];
   exact (f - g).norm_coe_le_norm x
 #align bounded_continuous_function.abs_diff_coe_le_dist BoundedContinuousFunction.abs_diff_coe_le_dist
 
@@ -2190,10 +2180,8 @@ instance : Algebra 𝕜 (α →ᵇ γ) :=
 <too large>
 Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.algebra_map_apply BoundedContinuousFunction.algebraMap_applyₓ'. -/
 @[simp]
-theorem algebraMap_apply (k : 𝕜) (a : α) : algebraMap 𝕜 (α →ᵇ γ) k a = k • 1 :=
-  by
-  rw [Algebra.algebraMap_eq_smul_one]
-  rfl
+theorem algebraMap_apply (k : 𝕜) (a : α) : algebraMap 𝕜 (α →ᵇ γ) k a = k • 1 := by
+  rw [Algebra.algebraMap_eq_smul_one]; rfl
 #align bounded_continuous_function.algebra_map_apply BoundedContinuousFunction.algebraMap_apply
 
 instance : NormedAlgebra 𝕜 (α →ᵇ γ) :=
@@ -2497,10 +2485,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.self_eq_nnreal_part_sub_nnreal_part_neg BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_negₓ'. -/
 /-- Decompose a bounded continuous function to its positive and negative parts. -/
 theorem self_eq_nnrealPart_sub_nnrealPart_neg (f : α →ᵇ ℝ) :
-    ⇑f = coe ∘ f.nnrealPart - coe ∘ (-f).nnrealPart :=
-  by
-  funext x
-  dsimp
+    ⇑f = coe ∘ f.nnrealPart - coe ∘ (-f).nnrealPart := by funext x; dsimp;
   simp only [max_zero_sub_max_neg_zero_eq_self]
 #align bounded_continuous_function.self_eq_nnreal_part_sub_nnreal_part_neg BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_neg
 
@@ -2513,10 +2498,7 @@ Case conversion may be inaccurate. Consider using '#align bounded_continuous_fun
 /-- Express the absolute value of a bounded continuous function in terms of its
 positive and negative parts. -/
 theorem abs_self_eq_nnrealPart_add_nnrealPart_neg (f : α →ᵇ ℝ) :
-    abs ∘ ⇑f = coe ∘ f.nnrealPart + coe ∘ (-f).nnrealPart :=
-  by
-  funext x
-  dsimp
+    abs ∘ ⇑f = coe ∘ f.nnrealPart + coe ∘ (-f).nnrealPart := by funext x; dsimp;
   simp only [max_zero_add_max_neg_zero_eq_abs_self]
 #align bounded_continuous_function.abs_self_eq_nnreal_part_add_nnreal_part_neg BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_neg
 

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

@@ -275,7 +275,6 @@ useless afterwards as it will be superseded by the general result that the dista
 in metric spaces. -/
 private theorem dist_nonneg' : 0 ≤ dist f g :=
   le_csInf dist_set_exists fun C => And.left
-#align bounded_continuous_function.dist_nonneg' bounded_continuous_function.dist_nonneg'
 
 /- warning: bounded_continuous_function.dist_le -> BoundedContinuousFunction.dist_le is a dubious translation:
 lean 3 declaration is
@@ -809,10 +808,7 @@ theorem extend_of_empty [IsEmpty α] (f : α ↪ δ) (g : α →ᵇ β) (h : δ
 #align bounded_continuous_function.extend_of_empty BoundedContinuousFunction.extend_of_empty
 
 /- warning: bounded_continuous_function.dist_extend_extend -> BoundedContinuousFunction.dist_extend_extend is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.dist_extend_extend BoundedContinuousFunction.dist_extend_extendₓ'. -/
 @[simp]
 theorem dist_extend_extend (f : α ↪ δ) (g₁ g₂ : α →ᵇ β) (h₁ h₂ : δ →ᵇ β) :
@@ -1817,10 +1813,7 @@ theorem coe_smul (c : 𝕜) (f : α →ᵇ β) : ⇑(c • f) = fun x => c • f
 #align bounded_continuous_function.coe_smul BoundedContinuousFunction.coe_smul
 
 /- warning: bounded_continuous_function.smul_apply -> BoundedContinuousFunction.smul_apply is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.smul_apply BoundedContinuousFunction.smul_applyₓ'. -/
 theorem smul_apply (c : 𝕜) (f : α →ᵇ β) (x : α) : (c • f) x = c • f x :=
   rfl
@@ -1894,10 +1887,7 @@ def evalClm (x : α) : (α →ᵇ β) →L[𝕜] β where
 #align bounded_continuous_function.eval_clm BoundedContinuousFunction.evalClm
 
 /- warning: bounded_continuous_function.eval_clm_apply -> BoundedContinuousFunction.evalClm_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.eval_clm_apply BoundedContinuousFunction.evalClm_applyₓ'. -/
 @[simp]
 theorem evalClm_apply (x : α) (f : α →ᵇ β) : evalClm 𝕜 x f = f x :=
@@ -1956,10 +1946,7 @@ variable [SeminormedAddCommGroup γ] [NormedSpace 𝕜 γ]
 variable (α)
 
 /- warning: continuous_linear_map.comp_left_continuous_bounded -> ContinuousLinearMap.compLeftContinuousBounded is a dubious translation:
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(SeminormedAddCommGroup.to_lipschitzAdd.{u2} β _inst_2)) (BoundedContinuousFunction.module.{u1, u3, u4} α γ 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5) (Ring.toSemiring.{u4} 𝕜 (NormedRing.toRing.{u4} 𝕜 (NormedCommRing.toNormedRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} γ (SeminormedAddCommGroup.toAddCommGroup.{u3} γ _inst_5)) (NormedSpace.toModule.{u4, u3} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_5 _inst_6) (ContinuousLinearMap.compLeftContinuousBounded._proof_2.{u4, u3} γ 𝕜 _inst_3 _inst_5 _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} γ _inst_5)))
-but is expected to have type
-  forall (α : Type.{u1}) {β : Type.{u2}} {γ : Type.{u3}} {𝕜 : Type.{u4}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : NontriviallyNormedField.{u4} 𝕜] [_inst_4 : NormedSpace.{u4, u2} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_2] [_inst_5 : SeminormedAddCommGroup.{u3} γ] [_inst_6 : NormedSpace.{u4, u3} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_5], (ContinuousLinearMap.{u4, u4, u2, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) γ (UniformSpace.toTopologicalSpace.{u3} γ (PseudoMetricSpace.toUniformSpace.{u3} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5))) (AddCommGroup.toAddCommMonoid.{u3} γ (SeminormedAddCommGroup.toAddCommGroup.{u3} γ _inst_5)) (NormedSpace.toModule.{u4, u2} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_2 _inst_4) (NormedSpace.toModule.{u4, u3} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_5 _inst_6)) -> (ContinuousLinearMap.{u4, u4, max u2 u1, max u3 u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} β _inst_2)) (BoundedContinuousFunction.{u1, u3} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5)) (UniformSpace.toTopologicalSpace.{max u1 u3} (BoundedContinuousFunction.{u1, u3} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5)) (PseudoMetricSpace.toUniformSpace.{max u1 u3} (BoundedContinuousFunction.{u1, u3} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5)) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u1, u3} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5)))) (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, u3} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5) (AddCommGroup.toAddCommMonoid.{u3} γ (SeminormedAddCommGroup.toAddCommGroup.{u3} γ _inst_5)) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} γ _inst_5)) (BoundedContinuousFunction.module.{u1, u2, u4} α β 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) (NormedSpace.toModule.{u4, u2} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_2 _inst_4) (NormedSpace.boundedSMul.{u4, u2} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_2 _inst_4) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} β _inst_2)) (BoundedContinuousFunction.module.{u1, u3, u4} α γ 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} γ (SeminormedAddCommGroup.toAddCommGroup.{u3} γ _inst_5)) (NormedSpace.toModule.{u4, u3} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_5 _inst_6) (NormedSpace.boundedSMul.{u4, u3} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_5 _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} γ _inst_5)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_left_continuous_bounded ContinuousLinearMap.compLeftContinuousBoundedₓ'. -/
 -- TODO does this work in the `has_bounded_smul` setting, too?
 /--
@@ -1979,10 +1966,7 @@ protected def ContinuousLinearMap.compLeftContinuousBounded (g : β →L[𝕜] 
 #align continuous_linear_map.comp_left_continuous_bounded ContinuousLinearMap.compLeftContinuousBounded
 
 /- warning: continuous_linear_map.comp_left_continuous_bounded_apply -> ContinuousLinearMap.compLeftContinuousBounded_apply is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_left_continuous_bounded_apply ContinuousLinearMap.compLeftContinuousBounded_applyₓ'. -/
 @[simp]
 theorem ContinuousLinearMap.compLeftContinuousBounded_apply (g : β →L[𝕜] γ) (f : α →ᵇ β) (x : α) :
@@ -2203,10 +2187,7 @@ instance : Algebra 𝕜 (α →ᵇ γ) :=
     smul_def' := fun c f => ext fun x => Algebra.smul_def' _ _ }
 
 /- warning: bounded_continuous_function.algebra_map_apply -> BoundedContinuousFunction.algebraMap_apply is a dubious translation:
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-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.algebra_map_apply BoundedContinuousFunction.algebraMap_applyₓ'. -/
 @[simp]
 theorem algebraMap_apply (k : 𝕜) (a : α) : algebraMap 𝕜 (α →ᵇ γ) k a = k • 1 :=
@@ -2423,10 +2404,7 @@ instance : Lattice (α →ᵇ β) :=
   { BoundedContinuousFunction.semilatticeSup, BoundedContinuousFunction.semilatticeInf with }
 
 /- warning: bounded_continuous_function.coe_fn_sup -> BoundedContinuousFunction.coeFn_sup is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_fn_sup BoundedContinuousFunction.coeFn_supₓ'. -/
 @[simp]
 theorem coeFn_sup (f g : α →ᵇ β) : ⇑(f ⊔ g) = f ⊔ g :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -1599,9 +1599,9 @@ theorem sub_apply : (f - g) x = f x - g x :=
 
 /- warning: bounded_continuous_function.mk_of_compact_neg -> BoundedContinuousFunction.mkOfCompact_neg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : CompactSpace.{u1} α _inst_1] (f : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))), Eq.{succ (max u1 u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 (Neg.neg.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (ContinuousMap.hasNeg.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} β _inst_2)) f)) (Neg.neg.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.hasNeg.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 f))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : CompactSpace.{u1} α _inst_1] (f : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))), Eq.{succ (max u1 u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 (Neg.neg.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (ContinuousMap.hasNeg.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} β _inst_2)) f)) (Neg.neg.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.hasNeg.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 f))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : CompactSpace.{u1} α _inst_1] (f : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))), Eq.{max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 (Neg.neg.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (ContinuousMap.instNegContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} β _inst_2)) f)) (Neg.neg.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.instNegBoundedContinuousFunctionToPseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 f))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : CompactSpace.{u1} α _inst_1] (f : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))), Eq.{max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 (Neg.neg.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (ContinuousMap.instNegContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} β _inst_2)) f)) (Neg.neg.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.instNegBoundedContinuousFunctionToPseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 f))
 Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.mk_of_compact_neg BoundedContinuousFunction.mkOfCompact_negₓ'. -/
 @[simp]
 theorem mkOfCompact_neg [CompactSpace α] (f : C(α, β)) : mkOfCompact (-f) = -mkOfCompact f :=
@@ -1610,9 +1610,9 @@ theorem mkOfCompact_neg [CompactSpace α] (f : C(α, β)) : mkOfCompact (-f) = -
 
 /- warning: bounded_continuous_function.mk_of_compact_sub -> BoundedContinuousFunction.mkOfCompact_sub is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : CompactSpace.{u1} α _inst_1] (f : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (g : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))), Eq.{succ (max u1 u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 (HSub.hSub.{max u1 u2, max u1 u2, max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (instHSub.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (ContinuousMap.hasSub.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (SubNegMonoid.toHasSub.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)))) (TopologicalAddGroup.to_continuousSub.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} β _inst_2)))) f g)) (HSub.hSub.{max u1 u2, max u1 u2, max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (instHSub.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.hasSub.{u1, u2} α β _inst_1 _inst_2)) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 f) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 g))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : CompactSpace.{u1} α _inst_1] (f : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (g : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))), Eq.{succ (max u1 u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 (HSub.hSub.{max u1 u2, max u1 u2, max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (instHSub.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (ContinuousMap.hasSub.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (SubNegMonoid.toHasSub.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)))) (TopologicalAddGroup.to_continuousSub.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} β _inst_2)))) f g)) (HSub.hSub.{max u1 u2, max u1 u2, max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (instHSub.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.hasSub.{u1, u2} α β _inst_1 _inst_2)) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 f) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 g))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : CompactSpace.{u1} α _inst_1] (f : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (g : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))), Eq.{max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 (HSub.hSub.{max u1 u2, max u1 u2, max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (instHSub.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (ContinuousMap.instSubContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (SubNegMonoid.toSub.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)))) (TopologicalAddGroup.to_continuousSub.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} β _inst_2)))) f g)) (HSub.hSub.{max u1 u2, max u1 u2, max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (instHSub.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.instSubBoundedContinuousFunctionToPseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2)) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 f) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 g))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : CompactSpace.{u1} α _inst_1] (f : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (g : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))), Eq.{max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 (HSub.hSub.{max u1 u2, max u1 u2, max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (instHSub.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (ContinuousMap.instSubContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (SubNegMonoid.toSub.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)))) (TopologicalAddGroup.to_continuousSub.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} β _inst_2)))) f g)) (HSub.hSub.{max u1 u2, max u1 u2, max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (instHSub.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.instSubBoundedContinuousFunctionToPseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2)) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 f) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 g))
 Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.mk_of_compact_sub BoundedContinuousFunction.mkOfCompact_subₓ'. -/
 @[simp]
 theorem mkOfCompact_sub [CompactSpace α] (f g : C(α, β)) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -254,8 +254,8 @@ Case conversion may be inaccurate. Consider using '#align bounded_continuous_fun
 theorem dist_set_exists : ∃ C, 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C :=
   by
   rcases f.bounded_range.union g.bounded_range with ⟨C, hC⟩
-  refine' ⟨max 0 C, le_max_left _ _, fun x => (hC _ _ _ _).trans (le_max_right _ _)⟩ <;> [left,
-      right] <;>
+  refine' ⟨max 0 C, le_max_left _ _, fun x => (hC _ _ _ _).trans (le_max_right _ _)⟩ <;>
+      [left;right] <;>
     apply mem_range_self
 #align bounded_continuous_function.dist_set_exists BoundedContinuousFunction.dist_set_exists
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Mario Carneiro, Yury Kudryashov, Heather Macbeth
 
 ! This file was ported from Lean 3 source module topology.continuous_function.bounded
-! leanprover-community/mathlib commit 5dc275ec639221ca4d5f56938eb966f6ad9bc89f
+! leanprover-community/mathlib commit 4280f5f32e16755ec7985ce11e189b6cd6ff6735
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,6 +18,9 @@ import Mathbin.Topology.MetricSpace.Equicontinuity
 /-!
 # Bounded continuous functions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The type of bounded continuous functions taking values in a metric space, with
 the uniform distance.
 

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

@@ -34,6 +34,7 @@ universe u v w
 
 variable {F : Type _} {α : Type u} {β : Type v} {γ : Type w}
 
+#print BoundedContinuousFunction /-
 /-- `α →ᵇ β` is the type of bounded continuous functions `α → β` from a topological space to a
 metric space.
 
@@ -45,12 +46,14 @@ structure BoundedContinuousFunction (α : Type u) (β : Type v) [TopologicalSpac
   [PseudoMetricSpace β] extends ContinuousMap α β : Type max u v where
   map_bounded' : ∃ C, ∀ x y, dist (to_fun x) (to_fun y) ≤ C
 #align bounded_continuous_function BoundedContinuousFunction
+-/
 
 -- mathport name: bounded_continuous_function
 scoped[BoundedContinuousFunction] infixr:25 " →ᵇ " => BoundedContinuousFunction
 
 section
 
+#print BoundedContinuousMapClass /-
 /-- `bounded_continuous_map_class F α β` states that `F` is a type of bounded continuous maps.
 
 You should also extend this typeclass when you extend `bounded_continuous_function`. -/
@@ -58,6 +61,7 @@ class BoundedContinuousMapClass (F α β : Type _) [TopologicalSpace α] [Pseudo
   ContinuousMapClass F α β where
   map_bounded (f : F) : ∃ C, ∀ x y, dist (f x) (f y) ≤ C
 #align bounded_continuous_map_class BoundedContinuousMapClass
+-/
 
 end
 
@@ -92,64 +96,130 @@ instance [BoundedContinuousMapClass F α β] : CoeTC F (α →ᵇ β) :=
       continuous_toFun := map_continuous f
       map_bounded' := map_bounded f }⟩
 
+/- warning: bounded_continuous_function.coe_to_continuous_fun -> BoundedContinuousFunction.coe_to_continuous_fun is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_to_continuous_fun BoundedContinuousFunction.coe_to_continuous_funₓ'. -/
 @[simp]
 theorem coe_to_continuous_fun (f : α →ᵇ β) : (f.toContinuousMap : α → β) = f :=
   rfl
 #align bounded_continuous_function.coe_to_continuous_fun BoundedContinuousFunction.coe_to_continuous_fun
 
+#print BoundedContinuousFunction.Simps.apply /-
 /-- See Note [custom simps projection]. We need to specify this projection explicitly in this case,
   because it is a composition of multiple projections. -/
 def Simps.apply (h : α →ᵇ β) : α → β :=
   h
 #align bounded_continuous_function.simps.apply BoundedContinuousFunction.Simps.apply
+-/
 
 initialize_simps_projections BoundedContinuousFunction (to_continuous_map_to_fun → apply)
 
+/- warning: bounded_continuous_function.bounded -> BoundedContinuousFunction.bounded is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.bounded BoundedContinuousFunction.boundedₓ'. -/
 protected theorem bounded (f : α →ᵇ β) : ∃ C, ∀ x y : α, dist (f x) (f y) ≤ C :=
   f.map_bounded'
 #align bounded_continuous_function.bounded BoundedContinuousFunction.bounded
 
+/- warning: bounded_continuous_function.continuous -> BoundedContinuousFunction.continuous is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.continuous BoundedContinuousFunction.continuousₓ'. -/
 protected theorem continuous (f : α →ᵇ β) : Continuous f :=
   f.toContinuousMap.Continuous
 #align bounded_continuous_function.continuous BoundedContinuousFunction.continuous
 
+/- warning: bounded_continuous_function.ext -> BoundedContinuousFunction.ext is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.ext BoundedContinuousFunction.extₓ'. -/
 @[ext]
 theorem ext (h : ∀ x, f x = g x) : f = g :=
   FunLike.ext _ _ h
 #align bounded_continuous_function.ext BoundedContinuousFunction.ext
 
+/- warning: bounded_continuous_function.bounded_range -> BoundedContinuousFunction.bounded_range is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.bounded_range BoundedContinuousFunction.bounded_rangeₓ'. -/
 theorem bounded_range (f : α →ᵇ β) : Bounded (range f) :=
   bounded_range_iff.2 f.Bounded
 #align bounded_continuous_function.bounded_range BoundedContinuousFunction.bounded_range
 
+/- warning: bounded_continuous_function.bounded_image -> BoundedContinuousFunction.bounded_image is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.bounded_image BoundedContinuousFunction.bounded_imageₓ'. -/
 theorem bounded_image (f : α →ᵇ β) (s : Set α) : Bounded (f '' s) :=
   f.bounded_range.mono <| image_subset_range _ _
 #align bounded_continuous_function.bounded_image BoundedContinuousFunction.bounded_image
 
+#print BoundedContinuousFunction.eq_of_empty /-
 theorem eq_of_empty [IsEmpty α] (f g : α →ᵇ β) : f = g :=
   ext <| IsEmpty.elim ‹_›
 #align bounded_continuous_function.eq_of_empty BoundedContinuousFunction.eq_of_empty
+-/
 
+/- warning: bounded_continuous_function.mk_of_bound -> BoundedContinuousFunction.mkOfBound is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.mk_of_bound BoundedContinuousFunction.mkOfBoundₓ'. -/
 /-- A continuous function with an explicit bound is a bounded continuous function. -/
 def mkOfBound (f : C(α, β)) (C : ℝ) (h : ∀ x y : α, dist (f x) (f y) ≤ C) : α →ᵇ β :=
   ⟨f, ⟨C, h⟩⟩
 #align bounded_continuous_function.mk_of_bound BoundedContinuousFunction.mkOfBound
 
+/- warning: bounded_continuous_function.mk_of_bound_coe -> BoundedContinuousFunction.mkOfBound_coe is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.mk_of_bound_coe BoundedContinuousFunction.mkOfBound_coeₓ'. -/
 @[simp]
 theorem mkOfBound_coe {f} {C} {h} : (mkOfBound f C h : α → β) = (f : α → β) :=
   rfl
 #align bounded_continuous_function.mk_of_bound_coe BoundedContinuousFunction.mkOfBound_coe
 
+#print BoundedContinuousFunction.mkOfCompact /-
 /-- A continuous function on a compact space is automatically a bounded continuous function. -/
 def mkOfCompact [CompactSpace α] (f : C(α, β)) : α →ᵇ β :=
   ⟨f, bounded_range_iff.1 (isCompact_range f.Continuous).Bounded⟩
 #align bounded_continuous_function.mk_of_compact BoundedContinuousFunction.mkOfCompact
+-/
 
+/- warning: bounded_continuous_function.mk_of_compact_apply -> BoundedContinuousFunction.mkOfCompact_apply is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] [_inst_4 : CompactSpace.{u1} α _inst_1] (f : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2))) (a : α), Eq.{succ u2} β (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 _inst_2 _inst_4 f) a) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2))) (fun (_x : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2))) => α -> β) (ContinuousMap.hasCoeToFun.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2))) f a)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.mk_of_compact_apply BoundedContinuousFunction.mkOfCompact_applyₓ'. -/
 @[simp]
 theorem mkOfCompact_apply [CompactSpace α] (f : C(α, β)) (a : α) : mkOfCompact f a = f a :=
   rfl
 #align bounded_continuous_function.mk_of_compact_apply BoundedContinuousFunction.mkOfCompact_apply
 
+/- warning: bounded_continuous_function.mk_of_discrete -> BoundedContinuousFunction.mkOfDiscrete is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] [_inst_4 : DiscreteTopology.{u1} α _inst_1] (f : α -> β) (C : Real), (forall (x : α) (y : α), LE.le.{0} Real Real.hasLe (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β _inst_2) (f x) (f y)) C) -> (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] [_inst_4 : DiscreteTopology.{u1} α _inst_1] (f : α -> β) (C : Real), (forall (x : α) (y : α), LE.le.{0} Real Real.instLEReal (Dist.dist.{u2} β (PseudoMetricSpace.toDist.{u2} β _inst_2) (f x) (f y)) C) -> (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.mk_of_discrete BoundedContinuousFunction.mkOfDiscreteₓ'. -/
 /-- If a function is bounded on a discrete space, it is automatically continuous,
 and therefore gives rise to an element of the type of bounded continuous functions -/
 @[simps]
@@ -162,10 +232,22 @@ def mkOfDiscrete [DiscreteTopology α] (f : α → β) (C : ℝ) (h : ∀ x y :
 instance : Dist (α →ᵇ β) :=
   ⟨fun f g => sInf { C | 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C }⟩
 
+/- warning: bounded_continuous_function.dist_eq -> BoundedContinuousFunction.dist_eq is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.dist_eq BoundedContinuousFunction.dist_eqₓ'. -/
 theorem dist_eq : dist f g = sInf { C | 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C } :=
   rfl
 #align bounded_continuous_function.dist_eq BoundedContinuousFunction.dist_eq
 
+/- warning: bounded_continuous_function.dist_set_exists -> BoundedContinuousFunction.dist_set_exists is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] {f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} {g : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2}, Exists.{1} Real (fun (C : Real) => And (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) C) (forall (x : α), LE.le.{0} Real Real.hasLe (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β _inst_2) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f x) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) g x)) C))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] {f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} {g : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2}, Exists.{1} Real (fun (C : Real) => And (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) C) (forall (x : α), LE.le.{0} Real Real.instLEReal (Dist.dist.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (PseudoMetricSpace.toDist.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 _inst_2 (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 _inst_2 (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2))) g x)) C))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.dist_set_exists BoundedContinuousFunction.dist_set_existsₓ'. -/
 theorem dist_set_exists : ∃ C, 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C :=
   by
   rcases f.bounded_range.union g.bounded_range with ⟨C, hC⟩
@@ -174,6 +256,12 @@ theorem dist_set_exists : ∃ C, 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C
     apply mem_range_self
 #align bounded_continuous_function.dist_set_exists BoundedContinuousFunction.dist_set_exists
 
+/- warning: bounded_continuous_function.dist_coe_le_dist -> BoundedContinuousFunction.dist_coe_le_dist is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] {f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} {g : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} (x : α), LE.le.{0} Real Real.hasLe (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β _inst_2) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f x) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) g x)) (Dist.dist.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.hasDist.{u1, u2} α β _inst_1 _inst_2) f g)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.dist_coe_le_dist BoundedContinuousFunction.dist_coe_le_distₓ'. -/
 /-- The pointwise distance is controlled by the distance between functions, by definition. -/
 theorem dist_coe_le_dist (x : α) : dist (f x) (g x) ≤ dist f g :=
   le_csInf dist_set_exists fun b hb => hb.2 x
@@ -186,16 +274,34 @@ private theorem dist_nonneg' : 0 ≤ dist f g :=
   le_csInf dist_set_exists fun C => And.left
 #align bounded_continuous_function.dist_nonneg' bounded_continuous_function.dist_nonneg'
 
+/- warning: bounded_continuous_function.dist_le -> BoundedContinuousFunction.dist_le is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.dist_le BoundedContinuousFunction.dist_leₓ'. -/
 /-- The distance between two functions is controlled by the supremum of the pointwise distances -/
 theorem dist_le (C0 : (0 : ℝ) ≤ C) : dist f g ≤ C ↔ ∀ x : α, dist (f x) (g x) ≤ C :=
   ⟨fun h x => le_trans (dist_coe_le_dist x) h, fun H => csInf_le ⟨0, fun C => And.left⟩ ⟨C0, H⟩⟩
 #align bounded_continuous_function.dist_le BoundedContinuousFunction.dist_le
 
+/- warning: bounded_continuous_function.dist_le_iff_of_nonempty -> BoundedContinuousFunction.dist_le_iff_of_nonempty is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] {f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} {g : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} {C : Real} [_inst_4 : Nonempty.{succ u1} α], Iff (LE.le.{0} Real Real.hasLe (Dist.dist.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.hasDist.{u1, u2} α β _inst_1 _inst_2) f g) C) (forall (x : α), LE.le.{0} Real Real.hasLe (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β _inst_2) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f x) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) g x)) C)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.dist_le_iff_of_nonempty BoundedContinuousFunction.dist_le_iff_of_nonemptyₓ'. -/
 theorem dist_le_iff_of_nonempty [Nonempty α] : dist f g ≤ C ↔ ∀ x, dist (f x) (g x) ≤ C :=
   ⟨fun h x => le_trans (dist_coe_le_dist x) h, fun w =>
     (dist_le (le_trans dist_nonneg (w (Nonempty.some ‹_›)))).mpr w⟩
 #align bounded_continuous_function.dist_le_iff_of_nonempty BoundedContinuousFunction.dist_le_iff_of_nonempty
 
+/- warning: bounded_continuous_function.dist_lt_of_nonempty_compact -> BoundedContinuousFunction.dist_lt_of_nonempty_compact is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.dist_lt_of_nonempty_compact BoundedContinuousFunction.dist_lt_of_nonempty_compactₓ'. -/
 theorem dist_lt_of_nonempty_compact [Nonempty α] [CompactSpace α]
     (w : ∀ x : α, dist (f x) (g x) < C) : dist f g < C :=
   by
@@ -205,6 +311,12 @@ theorem dist_lt_of_nonempty_compact [Nonempty α] [CompactSpace α]
   exact lt_of_le_of_lt (dist_le_iff_of_nonempty.mpr fun y => le y trivial) (w x)
 #align bounded_continuous_function.dist_lt_of_nonempty_compact BoundedContinuousFunction.dist_lt_of_nonempty_compact
 
+/- warning: bounded_continuous_function.dist_lt_iff_of_compact -> BoundedContinuousFunction.dist_lt_iff_of_compact is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] {f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} {g : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} {C : Real} [_inst_4 : CompactSpace.{u1} α _inst_1], (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) C) -> (Iff (LT.lt.{0} Real Real.hasLt (Dist.dist.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.hasDist.{u1, u2} α β _inst_1 _inst_2) f g) C) (forall (x : α), LT.lt.{0} Real Real.hasLt (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β _inst_2) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f x) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) g x)) C))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] {f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} {g : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} {C : Real} [_inst_4 : CompactSpace.{u1} α _inst_1], (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) C) -> (Iff (LT.lt.{0} Real Real.instLTReal (Dist.dist.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.instDistBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) f g) C) (forall (x : α), LT.lt.{0} Real Real.instLTReal (Dist.dist.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (PseudoMetricSpace.toDist.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 _inst_2 (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 _inst_2 (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2))) g x)) C))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.dist_lt_iff_of_compact BoundedContinuousFunction.dist_lt_iff_of_compactₓ'. -/
 theorem dist_lt_iff_of_compact [CompactSpace α] (C0 : (0 : ℝ) < C) :
     dist f g < C ↔ ∀ x : α, dist (f x) (g x) < C :=
   by
@@ -221,6 +333,12 @@ theorem dist_lt_iff_of_compact [CompactSpace α] (C0 : (0 : ℝ) < C) :
       exact csInf_le ⟨0, fun C => And.left⟩ ⟨le_rfl, fun x => False.elim (h (Nonempty.intro x))⟩
 #align bounded_continuous_function.dist_lt_iff_of_compact BoundedContinuousFunction.dist_lt_iff_of_compact
 
+/- warning: bounded_continuous_function.dist_lt_iff_of_nonempty_compact -> BoundedContinuousFunction.dist_lt_iff_of_nonempty_compact is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] {f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} {g : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} {C : Real} [_inst_4 : Nonempty.{succ u1} α] [_inst_5 : CompactSpace.{u1} α _inst_1], Iff (LT.lt.{0} Real Real.hasLt (Dist.dist.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.hasDist.{u1, u2} α β _inst_1 _inst_2) f g) C) (forall (x : α), LT.lt.{0} Real Real.hasLt (Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β _inst_2) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f x) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) g x)) C)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] {f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} {g : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} {C : Real} [_inst_4 : Nonempty.{succ u1} α] [_inst_5 : CompactSpace.{u1} α _inst_1], Iff (LT.lt.{0} Real Real.instLTReal (Dist.dist.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.instDistBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) f g) C) (forall (x : α), LT.lt.{0} Real Real.instLTReal (Dist.dist.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (PseudoMetricSpace.toDist.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 _inst_2 (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 _inst_2 (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2))) g x)) C)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.dist_lt_iff_of_nonempty_compact BoundedContinuousFunction.dist_lt_iff_of_nonempty_compactₓ'. -/
 theorem dist_lt_iff_of_nonempty_compact [Nonempty α] [CompactSpace α] :
     dist f g < C ↔ ∀ x : α, dist (f x) (g x) < C :=
   ⟨fun w x => lt_of_le_of_lt (dist_coe_le_dist x) w, dist_lt_of_nonempty_compact⟩
@@ -240,6 +358,12 @@ instance {α β} [TopologicalSpace α] [MetricSpace β] : MetricSpace (α →ᵇ
     where eq_of_dist_eq_zero f g hfg := by
     ext x <;> exact eq_of_dist_eq_zero (le_antisymm (hfg ▸ dist_coe_le_dist _) dist_nonneg)
 
+/- warning: bounded_continuous_function.nndist_eq -> BoundedContinuousFunction.nndist_eq is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.nndist_eq BoundedContinuousFunction.nndist_eqₓ'. -/
 theorem nndist_eq : nndist f g = sInf { C | ∀ x : α, nndist (f x) (g x) ≤ C } :=
   Subtype.ext <|
     dist_eq.trans <| by
@@ -247,19 +371,43 @@ theorem nndist_eq : nndist f g = sInf { C | ∀ x : α, nndist (f x) (g x) ≤ C
       simp_rw [mem_set_of_eq, ← NNReal.coe_le_coe, Subtype.coe_mk, exists_prop, coe_nndist]
 #align bounded_continuous_function.nndist_eq BoundedContinuousFunction.nndist_eq
 
+/- warning: bounded_continuous_function.nndist_set_exists -> BoundedContinuousFunction.nndist_set_exists is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] {f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} {g : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2}, Exists.{1} NNReal (fun (C : NNReal) => forall (x : α), 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} β (PseudoMetricSpace.toNNDist.{u2} β _inst_2) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f x) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) g x)) C)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.nndist_set_exists BoundedContinuousFunction.nndist_set_existsₓ'. -/
 theorem nndist_set_exists : ∃ C, ∀ x : α, nndist (f x) (g x) ≤ C :=
   Subtype.exists.mpr <| dist_set_exists.imp fun a ⟨ha, h⟩ => ⟨ha, h⟩
 #align bounded_continuous_function.nndist_set_exists BoundedContinuousFunction.nndist_set_exists
 
+/- warning: bounded_continuous_function.nndist_coe_le_nndist -> BoundedContinuousFunction.nndist_coe_le_nndist is a dubious translation:
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+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] {f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} {g : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} (x : α), 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} β (PseudoMetricSpace.toNNDist.{u2} β _inst_2) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f x) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) g x)) (NNDist.nndist.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (PseudoMetricSpace.toNNDist.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.pseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2)) f g)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] {f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} {g : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} (x : α), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNDist.nndist.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (PseudoMetricSpace.toNNDist.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 _inst_2 (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 _inst_2 (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2))) g x)) (NNDist.nndist.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (PseudoMetricSpace.toNNDist.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2)) f g)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.nndist_coe_le_nndist BoundedContinuousFunction.nndist_coe_le_nndistₓ'. -/
 theorem nndist_coe_le_nndist (x : α) : nndist (f x) (g x) ≤ nndist f g :=
   dist_coe_le_dist x
 #align bounded_continuous_function.nndist_coe_le_nndist BoundedContinuousFunction.nndist_coe_le_nndist
 
+/- warning: bounded_continuous_function.dist_zero_of_empty -> BoundedContinuousFunction.dist_zero_of_empty is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] {f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} {g : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} [_inst_4 : IsEmpty.{succ u1} α], Eq.{1} Real (Dist.dist.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.hasDist.{u1, u2} α β _inst_1 _inst_2) f g) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] {f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} {g : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} [_inst_4 : IsEmpty.{succ u1} α], Eq.{1} Real (Dist.dist.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.instDistBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) f g) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.dist_zero_of_empty BoundedContinuousFunction.dist_zero_of_emptyₓ'. -/
 /-- On an empty space, bounded continuous functions are at distance 0 -/
 theorem dist_zero_of_empty [IsEmpty α] : dist f g = 0 := by
   rw [(ext isEmptyElim : f = g), dist_self]
 #align bounded_continuous_function.dist_zero_of_empty BoundedContinuousFunction.dist_zero_of_empty
 
+/- warning: bounded_continuous_function.dist_eq_supr -> BoundedContinuousFunction.dist_eq_iSup is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] {f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} {g : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2}, Eq.{1} Real (Dist.dist.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.hasDist.{u1, u2} α β _inst_1 _inst_2) f g) (iSup.{0, succ u1} Real Real.hasSup α (fun (x : α) => Dist.dist.{u2} β (PseudoMetricSpace.toHasDist.{u2} β _inst_2) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f x) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) g x)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] {f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} {g : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2}, Eq.{1} Real (Dist.dist.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.instDistBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) f g) (iSup.{0, succ u1} Real Real.instSupSetReal α (fun (x : α) => Dist.dist.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (PseudoMetricSpace.toDist.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 _inst_2 (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 _inst_2 (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2))) g x)))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.dist_eq_supr BoundedContinuousFunction.dist_eq_iSupₓ'. -/
 theorem dist_eq_iSup : dist f g = ⨆ x : α, dist (f x) (g x) :=
   by
   cases isEmpty_or_nonempty α; · rw [iSup_of_empty', Real.sSup_empty, dist_zero_of_empty]
@@ -267,10 +415,22 @@ theorem dist_eq_iSup : dist f g = ⨆ x : α, dist (f x) (g x) :=
   exact dist_set_exists.imp fun C hC => forall_range_iff.2 hC.2
 #align bounded_continuous_function.dist_eq_supr BoundedContinuousFunction.dist_eq_iSup
 
+/- warning: bounded_continuous_function.nndist_eq_supr -> BoundedContinuousFunction.nndist_eq_iSup is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.nndist_eq_supr BoundedContinuousFunction.nndist_eq_iSupₓ'. -/
 theorem nndist_eq_iSup : nndist f g = ⨆ x : α, nndist (f x) (g x) :=
   Subtype.ext <| dist_eq_iSup.trans <| by simp_rw [NNReal.coe_iSup, coe_nndist]
 #align bounded_continuous_function.nndist_eq_supr BoundedContinuousFunction.nndist_eq_iSup
 
+/- warning: bounded_continuous_function.tendsto_iff_tendsto_uniformly -> BoundedContinuousFunction.tendsto_iff_tendstoUniformly is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] {ι : Type.{u3}} {F : ι -> (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2)} {f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2} {l : Filter.{u3} ι}, Iff (Filter.Tendsto.{u3, max u1 u2} ι (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) F l (nhds.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.pseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2))) f)) (TendstoUniformly.{u1, u2, u3} α β ι (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2) (fun (i : ι) => coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) (F i)) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f) l)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.tendsto_iff_tendsto_uniformly BoundedContinuousFunction.tendsto_iff_tendstoUniformlyₓ'. -/
 theorem tendsto_iff_tendstoUniformly {ι : Type _} {F : ι → α →ᵇ β} {f : α →ᵇ β} {l : Filter ι} :
     Tendsto F l (𝓝 f) ↔ TendstoUniformly (fun i => F i) f l :=
   Iff.intro
@@ -288,6 +448,12 @@ theorem tendsto_iff_tendstoUniformly {ι : Type _} {F : ι → α →ᵇ β} {f
             (half_lt_self ε_pos))
 #align bounded_continuous_function.tendsto_iff_tendsto_uniformly BoundedContinuousFunction.tendsto_iff_tendstoUniformly
 
+/- warning: bounded_continuous_function.inducing_coe_fn -> BoundedContinuousFunction.inducing_coeFn is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.inducing_coe_fn BoundedContinuousFunction.inducing_coeFnₓ'. -/
 /-- The topology on `α →ᵇ β` is exactly the topology induced by the natural map to `α →ᵤ β`. -/
 theorem inducing_coeFn : Inducing (UniformFun.ofFun ∘ coeFn : (α →ᵇ β) → α →ᵤ β) :=
   by
@@ -298,6 +464,12 @@ theorem inducing_coeFn : Inducing (UniformFun.ofFun ∘ coeFn : (α →ᵇ β) 
   rfl
 #align bounded_continuous_function.inducing_coe_fn BoundedContinuousFunction.inducing_coeFn
 
+/- warning: bounded_continuous_function.embedding_coe_fn -> BoundedContinuousFunction.embedding_coeFn is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.embedding_coe_fn BoundedContinuousFunction.embedding_coeFnₓ'. -/
 -- TODO: upgrade to a `uniform_embedding`
 theorem embedding_coeFn : Embedding (UniformFun.ofFun ∘ coeFn : (α →ᵇ β) → α →ᵤ β) :=
   ⟨inducing_coeFn, fun f g h => ext fun x => congr_fun h x⟩
@@ -305,14 +477,22 @@ theorem embedding_coeFn : Embedding (UniformFun.ofFun ∘ coeFn : (α →ᵇ β)
 
 variable (α) {β}
 
+#print BoundedContinuousFunction.const /-
 /-- Constant as a continuous bounded function. -/
 @[simps (config := { fullyApplied := false })]
 def const (b : β) : α →ᵇ β :=
   ⟨ContinuousMap.const α b, 0, by simp [le_rfl]⟩
 #align bounded_continuous_function.const BoundedContinuousFunction.const
+-/
 
 variable {α}
 
+/- warning: bounded_continuous_function.const_apply' -> BoundedContinuousFunction.const_apply' is a dubious translation:
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+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] (a : α) (b : β), Eq.{succ u2} β (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.const.{u1, u2} α β _inst_1 _inst_2 b) a) b
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] (a : α) (b : β), Eq.{succ u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 _inst_2 (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2))) (BoundedContinuousFunction.const.{u1, u2} α β _inst_1 _inst_2 b) a) b
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.const_apply' BoundedContinuousFunction.const_apply'ₓ'. -/
 theorem const_apply' (a : α) (b : β) : (const α b : α → β) a = b :=
   rfl
 #align bounded_continuous_function.const_apply' BoundedContinuousFunction.const_apply'
@@ -321,24 +501,54 @@ theorem const_apply' (a : α) (b : β) : (const α b : α → β) a = b :=
 instance [Inhabited β] : Inhabited (α →ᵇ β) :=
   ⟨const α default⟩
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.lipschitz_evalx BoundedContinuousFunction.lipschitz_evalxₓ'. -/
 theorem lipschitz_evalx (x : α) : LipschitzWith 1 fun f : α →ᵇ β => f x :=
   LipschitzWith.mk_one fun f g => dist_coe_le_dist x
 #align bounded_continuous_function.lipschitz_evalx BoundedContinuousFunction.lipschitz_evalx
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.uniform_continuous_coe BoundedContinuousFunction.uniformContinuous_coeₓ'. -/
 theorem uniformContinuous_coe : @UniformContinuous (α →ᵇ β) (α → β) _ _ coeFn :=
   uniformContinuous_pi.2 fun x => (lipschitz_evalx x).UniformContinuous
 #align bounded_continuous_function.uniform_continuous_coe BoundedContinuousFunction.uniformContinuous_coe
 
+/- warning: bounded_continuous_function.continuous_coe -> BoundedContinuousFunction.continuous_coe is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.continuous_coe BoundedContinuousFunction.continuous_coeₓ'. -/
 theorem continuous_coe : Continuous fun (f : α →ᵇ β) x => f x :=
   UniformContinuous.continuous uniformContinuous_coe
 #align bounded_continuous_function.continuous_coe BoundedContinuousFunction.continuous_coe
 
+/- warning: bounded_continuous_function.continuous_eval_const -> BoundedContinuousFunction.continuous_eval_const is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] {x : α}, Continuous.{max u1 u2, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) β (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.pseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2))) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (fun (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f x)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] {x : α}, Continuous.{max u1 u2, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2))) (UniformSpace.toTopologicalSpace.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (PseudoMetricSpace.toUniformSpace.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) _inst_2)) (fun (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 _inst_2 (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2))) f x)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.continuous_eval_const BoundedContinuousFunction.continuous_eval_constₓ'. -/
 /-- When `x` is fixed, `(f : α →ᵇ β) ↦ f x` is continuous -/
 @[continuity]
 theorem continuous_eval_const {x : α} : Continuous fun f : α →ᵇ β => f x :=
   (continuous_apply x).comp continuous_coe
 #align bounded_continuous_function.continuous_eval_const BoundedContinuousFunction.continuous_eval_const
 
+/- warning: bounded_continuous_function.continuous_eval -> BoundedContinuousFunction.continuous_eval is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β], Continuous.{max u1 u2, u2} (Prod.{max u1 u2, u1} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α) β (Prod.topologicalSpace.{max u1 u2, u1} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.pseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2))) _inst_1) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (fun (p : Prod.{max u1 u2, u1} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α) => coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) (Prod.fst.{max u1 u2, u1} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α p) (Prod.snd.{max u1 u2, u1} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α p))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β], Continuous.{max u1 u2, u2} (Prod.{max u2 u1, u1} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α) β (instTopologicalSpaceProd.{max u1 u2, u1} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2))) _inst_1) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (fun (p : Prod.{max u2 u1, u1} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 _inst_2 (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2))) (Prod.fst.{max u1 u2, u1} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α p) (Prod.snd.{max u1 u2, u1} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) α p))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.continuous_eval BoundedContinuousFunction.continuous_evalₓ'. -/
 /-- The evaluation map is continuous, as a joint function of `u` and `x` -/
 @[continuity]
 theorem continuous_eval : Continuous fun p : (α →ᵇ β) × α => p.1 p.2 :=
@@ -383,50 +593,91 @@ instance [CompleteSpace β] : CompleteSpace (α →ᵇ β) :=
       refine' tendsto_iff_dist_tendsto_zero.2 (squeeze_zero (fun _ => dist_nonneg) _ b_lim)
       exact fun N => (dist_le (b0 _)).2 fun x => fF_bdd x N
 
+#print BoundedContinuousFunction.compContinuous /-
 /-- Composition of a bounded continuous function and a continuous function. -/
 def compContinuous {δ : Type _} [TopologicalSpace δ] (f : α →ᵇ β) (g : C(δ, α)) : δ →ᵇ β
     where
   toContinuousMap := f.1.comp g
   map_bounded' := f.map_bounded'.imp fun C hC x y => hC _ _
 #align bounded_continuous_function.comp_continuous BoundedContinuousFunction.compContinuous
+-/
 
+/- warning: bounded_continuous_function.coe_comp_continuous -> BoundedContinuousFunction.coe_compContinuous is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] {δ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} δ] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (g : ContinuousMap.{u3, u1} δ α _inst_4 _inst_1), Eq.{max (succ u3) (succ u2)} (δ -> β) (coeFn.{succ (max u3 u2), max (succ u3) (succ u2)} (BoundedContinuousFunction.{u3, u2} δ β _inst_4 _inst_2) (fun (_x : BoundedContinuousFunction.{u3, u2} δ β _inst_4 _inst_2) => δ -> β) (BoundedContinuousFunction.hasCoeToFun.{u3, u2} δ β _inst_4 _inst_2) (BoundedContinuousFunction.compContinuous.{u1, u2, u3} α β _inst_1 _inst_2 δ _inst_4 f g)) (Function.comp.{succ u3, succ u1, succ u2} δ α β (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (ContinuousMap.{u3, u1} δ α _inst_4 _inst_1) (fun (_x : ContinuousMap.{u3, u1} δ α _inst_4 _inst_1) => δ -> α) (ContinuousMap.hasCoeToFun.{u3, u1} δ α _inst_4 _inst_1) g))
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_comp_continuous BoundedContinuousFunction.coe_compContinuousₓ'. -/
 @[simp]
 theorem coe_compContinuous {δ : Type _} [TopologicalSpace δ] (f : α →ᵇ β) (g : C(δ, α)) :
     coeFn (f.comp_continuous g) = f ∘ g :=
   rfl
 #align bounded_continuous_function.coe_comp_continuous BoundedContinuousFunction.coe_compContinuous
 
+/- warning: bounded_continuous_function.comp_continuous_apply -> BoundedContinuousFunction.compContinuous_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.comp_continuous_apply BoundedContinuousFunction.compContinuous_applyₓ'. -/
 @[simp]
 theorem compContinuous_apply {δ : Type _} [TopologicalSpace δ] (f : α →ᵇ β) (g : C(δ, α)) (x : δ) :
     f.comp_continuous g x = f (g x) :=
   rfl
 #align bounded_continuous_function.comp_continuous_apply BoundedContinuousFunction.compContinuous_apply
 
+/- warning: bounded_continuous_function.lipschitz_comp_continuous -> BoundedContinuousFunction.lipschitz_compContinuous is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.lipschitz_comp_continuous BoundedContinuousFunction.lipschitz_compContinuousₓ'. -/
 theorem lipschitz_compContinuous {δ : Type _} [TopologicalSpace δ] (g : C(δ, α)) :
     LipschitzWith 1 fun f : α →ᵇ β => f.comp_continuous g :=
   LipschitzWith.mk_one fun f₁ f₂ => (dist_le dist_nonneg).2 fun x => dist_coe_le_dist (g x)
 #align bounded_continuous_function.lipschitz_comp_continuous BoundedContinuousFunction.lipschitz_compContinuous
 
+/- warning: bounded_continuous_function.continuous_comp_continuous -> BoundedContinuousFunction.continuous_compContinuous is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] {δ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} δ] (g : ContinuousMap.{u3, u1} δ α _inst_4 _inst_1), Continuous.{max u1 u2, max u3 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.{u3, u2} δ β _inst_4 _inst_2) (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.pseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2))) (UniformSpace.toTopologicalSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} δ β _inst_4 _inst_2) (PseudoMetricSpace.toUniformSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} δ β _inst_4 _inst_2) (BoundedContinuousFunction.pseudoMetricSpace.{u3, u2} δ β _inst_4 _inst_2))) (fun (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => BoundedContinuousFunction.compContinuous.{u1, u2, u3} α β _inst_1 _inst_2 δ _inst_4 f g)
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : PseudoMetricSpace.{u3} β] {δ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} δ] (g : ContinuousMap.{u1, u2} δ α _inst_4 _inst_1), Continuous.{max u2 u3, max u3 u1} (BoundedContinuousFunction.{u2, u3} α β _inst_1 _inst_2) (BoundedContinuousFunction.{u1, u3} δ β _inst_4 _inst_2) (UniformSpace.toTopologicalSpace.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α β _inst_1 _inst_2) (PseudoMetricSpace.toUniformSpace.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α β _inst_1 _inst_2) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u2, u3} α β _inst_1 _inst_2))) (UniformSpace.toTopologicalSpace.{max u3 u1} (BoundedContinuousFunction.{u1, u3} δ β _inst_4 _inst_2) (PseudoMetricSpace.toUniformSpace.{max u3 u1} (BoundedContinuousFunction.{u1, u3} δ β _inst_4 _inst_2) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u1, u3} δ β _inst_4 _inst_2))) (fun (f : BoundedContinuousFunction.{u2, u3} α β _inst_1 _inst_2) => BoundedContinuousFunction.compContinuous.{u2, u3, u1} α β _inst_1 _inst_2 δ _inst_4 f g)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.continuous_comp_continuous BoundedContinuousFunction.continuous_compContinuousₓ'. -/
 theorem continuous_compContinuous {δ : Type _} [TopologicalSpace δ] (g : C(δ, α)) :
     Continuous fun f : α →ᵇ β => f.comp_continuous g :=
   (lipschitz_compContinuous g).Continuous
 #align bounded_continuous_function.continuous_comp_continuous BoundedContinuousFunction.continuous_compContinuous
 
+#print BoundedContinuousFunction.restrict /-
 /-- Restrict a bounded continuous function to a set. -/
 def restrict (f : α →ᵇ β) (s : Set α) : s →ᵇ β :=
   f.comp_continuous <| (ContinuousMap.id _).restrict s
 #align bounded_continuous_function.restrict BoundedContinuousFunction.restrict
+-/
 
+/- warning: bounded_continuous_function.coe_restrict -> BoundedContinuousFunction.coe_restrict is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (s : Set.{u1} α), Eq.{max (succ u1) (succ u2)} ((coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) -> β) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β (Subtype.topologicalSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β (Subtype.topologicalSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) _inst_2) => (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β (Subtype.topologicalSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) _inst_2) (BoundedContinuousFunction.restrict.{u1, u2} α β _inst_1 _inst_2 f s)) (Function.comp.{succ u1, succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α β (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s)))))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_restrict BoundedContinuousFunction.coe_restrictₓ'. -/
 @[simp]
 theorem coe_restrict (f : α →ᵇ β) (s : Set α) : coeFn (f.restrict s) = f ∘ coe :=
   rfl
 #align bounded_continuous_function.coe_restrict BoundedContinuousFunction.coe_restrict
 
+/- warning: bounded_continuous_function.restrict_apply -> BoundedContinuousFunction.restrict_apply is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (s : Set.{u1} α) (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s), Eq.{succ u2} β (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β (Subtype.topologicalSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β (Subtype.topologicalSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) _inst_2) => (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β (Subtype.topologicalSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1) _inst_2) (BoundedContinuousFunction.restrict.{u1, u2} α β _inst_1 _inst_2 f s) x) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.restrict_apply BoundedContinuousFunction.restrict_applyₓ'. -/
 @[simp]
 theorem restrict_apply (f : α →ᵇ β) (s : Set α) (x : s) : f.restrict s x = f x :=
   rfl
 #align bounded_continuous_function.restrict_apply BoundedContinuousFunction.restrict_apply
 
+#print BoundedContinuousFunction.comp /-
 /-- Composition (in the target) of a bounded continuous function with a Lipschitz map again
 gives a bounded continuous function -/
 def comp (G : β → γ) {C : ℝ≥0} (H : LipschitzWith C G) (f : α →ᵇ β) : α →ᵇ γ :=
@@ -439,7 +690,14 @@ def comp (G : β → γ) {C : ℝ≥0} (H : LipschitzWith C G) (f : α →ᵇ β
         _ ≤ max C 0 * D := mul_le_mul_of_nonneg_left (hD _ _) (le_max_right C 0)
         ⟩⟩
 #align bounded_continuous_function.comp BoundedContinuousFunction.comp
+-/
 
+/- warning: bounded_continuous_function.lipschitz_comp -> BoundedContinuousFunction.lipschitz_comp is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] [_inst_3 : PseudoMetricSpace.{u3} γ] {G : β -> γ} {C : NNReal} (H : LipschitzWith.{u2, u3} β γ (PseudoMetricSpace.toPseudoEMetricSpace.{u2} β _inst_2) (PseudoMetricSpace.toPseudoEMetricSpace.{u3} γ _inst_3) C G), LipschitzWith.{max u1 u2, max u1 u3} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.{u1, u3} α γ _inst_1 _inst_3) (PseudoMetricSpace.toPseudoEMetricSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.pseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2)) (PseudoMetricSpace.toPseudoEMetricSpace.{max u1 u3} (BoundedContinuousFunction.{u1, u3} α γ _inst_1 _inst_3) (BoundedContinuousFunction.pseudoMetricSpace.{u1, u3} α γ _inst_1 _inst_3)) C (BoundedContinuousFunction.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 G C H)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] [_inst_3 : PseudoMetricSpace.{u3} γ] {G : β -> γ} {C : NNReal} (H : LipschitzWith.{u2, u3} β γ (PseudoMetricSpace.toPseudoEMetricSpace.{u2} β _inst_2) (PseudoMetricSpace.toPseudoEMetricSpace.{u3} γ _inst_3) C G), LipschitzWith.{max u1 u2, max u1 u3} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.{u1, u3} α γ _inst_1 _inst_3) (PseudoMetricSpace.toPseudoEMetricSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2)) (PseudoMetricSpace.toPseudoEMetricSpace.{max u1 u3} (BoundedContinuousFunction.{u1, u3} α γ _inst_1 _inst_3) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u1, u3} α γ _inst_1 _inst_3)) C (BoundedContinuousFunction.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 G C H)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.lipschitz_comp BoundedContinuousFunction.lipschitz_compₓ'. -/
 /-- The composition operator (in the target) with a Lipschitz map is Lipschitz -/
 theorem lipschitz_comp {G : β → γ} {C : ℝ≥0} (H : LipschitzWith C G) :
     LipschitzWith C (comp G H : (α →ᵇ β) → α →ᵇ γ) :=
@@ -451,18 +709,36 @@ theorem lipschitz_comp {G : β → γ} {C : ℝ≥0} (H : LipschitzWith C G) :
         
 #align bounded_continuous_function.lipschitz_comp BoundedContinuousFunction.lipschitz_comp
 
+/- warning: bounded_continuous_function.uniform_continuous_comp -> BoundedContinuousFunction.uniformContinuous_comp is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] [_inst_3 : PseudoMetricSpace.{u3} γ] {G : β -> γ} {C : NNReal} (H : LipschitzWith.{u2, u3} β γ (PseudoMetricSpace.toPseudoEMetricSpace.{u2} β _inst_2) (PseudoMetricSpace.toPseudoEMetricSpace.{u3} γ _inst_3) C G), UniformContinuous.{max u1 u2, max u1 u3} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.{u1, u3} α γ _inst_1 _inst_3) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.pseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2)) (PseudoMetricSpace.toUniformSpace.{max u1 u3} (BoundedContinuousFunction.{u1, u3} α γ _inst_1 _inst_3) (BoundedContinuousFunction.pseudoMetricSpace.{u1, u3} α γ _inst_1 _inst_3)) (BoundedContinuousFunction.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 G C H)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.uniform_continuous_comp BoundedContinuousFunction.uniformContinuous_compₓ'. -/
 /-- The composition operator (in the target) with a Lipschitz map is uniformly continuous -/
 theorem uniformContinuous_comp {G : β → γ} {C : ℝ≥0} (H : LipschitzWith C G) :
     UniformContinuous (comp G H : (α →ᵇ β) → α →ᵇ γ) :=
   (lipschitz_comp H).UniformContinuous
 #align bounded_continuous_function.uniform_continuous_comp BoundedContinuousFunction.uniformContinuous_comp
 
+/- warning: bounded_continuous_function.continuous_comp -> BoundedContinuousFunction.continuous_comp is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] [_inst_3 : PseudoMetricSpace.{u3} γ] {G : β -> γ} {C : NNReal} (H : LipschitzWith.{u2, u3} β γ (PseudoMetricSpace.toPseudoEMetricSpace.{u2} β _inst_2) (PseudoMetricSpace.toPseudoEMetricSpace.{u3} γ _inst_3) C G), Continuous.{max u1 u2, max u1 u3} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.{u1, u3} α γ _inst_1 _inst_3) (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.pseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2))) (UniformSpace.toTopologicalSpace.{max u1 u3} (BoundedContinuousFunction.{u1, u3} α γ _inst_1 _inst_3) (PseudoMetricSpace.toUniformSpace.{max u1 u3} (BoundedContinuousFunction.{u1, u3} α γ _inst_1 _inst_3) (BoundedContinuousFunction.pseudoMetricSpace.{u1, u3} α γ _inst_1 _inst_3))) (BoundedContinuousFunction.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 G C H)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.continuous_comp BoundedContinuousFunction.continuous_compₓ'. -/
 /-- The composition operator (in the target) with a Lipschitz map is continuous -/
 theorem continuous_comp {G : β → γ} {C : ℝ≥0} (H : LipschitzWith C G) :
     Continuous (comp G H : (α →ᵇ β) → α →ᵇ γ) :=
   (lipschitz_comp H).Continuous
 #align bounded_continuous_function.continuous_comp BoundedContinuousFunction.continuous_comp
 
+/- warning: bounded_continuous_function.cod_restrict -> BoundedContinuousFunction.codRestrict is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.cod_restrict BoundedContinuousFunction.codRestrictₓ'. -/
 /-- Restriction (in the target) of a bounded continuous function taking values in a subset -/
 def codRestrict (s : Set β) (f : α →ᵇ β) (H : ∀ x, f x ∈ s) : α →ᵇ s :=
   ⟨⟨s.codRestrict f H, f.Continuous.subtype_mk _⟩, f.Bounded⟩
@@ -472,6 +748,7 @@ section Extend
 
 variable {δ : Type _} [TopologicalSpace δ] [DiscreteTopology δ]
 
+#print BoundedContinuousFunction.extend /-
 /-- A version of `function.extend` for bounded continuous maps. We assume that the domain has
 discrete topology, so we only need to verify boundedness. -/
 def extend (f : α ↪ δ) (g : α →ᵇ β) (h : δ →ᵇ β) : δ →ᵇ β
@@ -483,26 +760,57 @@ def extend (f : α ↪ δ) (g : α →ᵇ β) (h : δ →ᵇ β) : δ →ᵇ β
     rw [← bounded_range_iff, range_extend f.injective, Metric.bounded_union]
     exact ⟨g.bounded_range, h.bounded_image _⟩
 #align bounded_continuous_function.extend BoundedContinuousFunction.extend
+-/
 
+/- warning: bounded_continuous_function.extend_apply -> BoundedContinuousFunction.extend_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.extend_apply BoundedContinuousFunction.extend_applyₓ'. -/
 @[simp]
 theorem extend_apply (f : α ↪ δ) (g : α →ᵇ β) (h : δ →ᵇ β) (x : α) : extend f g h (f x) = g x :=
   f.Injective.extend_apply _ _ _
 #align bounded_continuous_function.extend_apply BoundedContinuousFunction.extend_apply
 
+/- warning: bounded_continuous_function.extend_comp -> BoundedContinuousFunction.extend_comp is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.extend_comp BoundedContinuousFunction.extend_compₓ'. -/
 @[simp]
 theorem extend_comp (f : α ↪ δ) (g : α →ᵇ β) (h : δ →ᵇ β) : extend f g h ∘ f = g :=
   extend_comp f.Injective _ _
 #align bounded_continuous_function.extend_comp BoundedContinuousFunction.extend_comp
 
+/- warning: bounded_continuous_function.extend_apply' -> BoundedContinuousFunction.extend_apply' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.extend_apply' BoundedContinuousFunction.extend_apply'ₓ'. -/
 theorem extend_apply' {f : α ↪ δ} {x : δ} (hx : x ∉ range f) (g : α →ᵇ β) (h : δ →ᵇ β) :
     extend f g h x = h x :=
   extend_apply' _ _ _ hx
 #align bounded_continuous_function.extend_apply' BoundedContinuousFunction.extend_apply'
 
+/- warning: bounded_continuous_function.extend_of_empty -> BoundedContinuousFunction.extend_of_empty is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.extend_of_empty BoundedContinuousFunction.extend_of_emptyₓ'. -/
 theorem extend_of_empty [IsEmpty α] (f : α ↪ δ) (g : α →ᵇ β) (h : δ →ᵇ β) : extend f g h = h :=
   FunLike.coe_injective <| Function.extend_of_isEmpty f g h
 #align bounded_continuous_function.extend_of_empty BoundedContinuousFunction.extend_of_empty
 
+/- warning: bounded_continuous_function.dist_extend_extend -> BoundedContinuousFunction.dist_extend_extend is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.dist_extend_extend BoundedContinuousFunction.dist_extend_extendₓ'. -/
 @[simp]
 theorem dist_extend_extend (f : α ↪ δ) (g₁ g₂ : α →ᵇ β) (h₁ h₂ : δ →ᵇ β) :
     dist (g₁.extend f h₁) (g₂.extend f h₂) =
@@ -530,6 +838,12 @@ theorem dist_extend_extend (f : α ↪ δ) (g₁ g₂ : α →ᵇ β) (h₁ h₂
       
 #align bounded_continuous_function.dist_extend_extend BoundedContinuousFunction.dist_extend_extend
 
+/- warning: bounded_continuous_function.isometry_extend -> BoundedContinuousFunction.isometry_extend is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] {δ : Type.{u3}} [_inst_4 : TopologicalSpace.{u3} δ] [_inst_5 : DiscreteTopology.{u3} δ _inst_4] (f : Function.Embedding.{succ u1, succ u3} α δ) (h : BoundedContinuousFunction.{u3, u2} δ β _inst_4 _inst_2), Isometry.{max u1 u2, max u3 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.{u3, u2} δ β _inst_4 _inst_2) (PseudoMetricSpace.toPseudoEMetricSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.pseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2)) (PseudoMetricSpace.toPseudoEMetricSpace.{max u3 u2} (BoundedContinuousFunction.{u3, u2} δ β _inst_4 _inst_2) (BoundedContinuousFunction.pseudoMetricSpace.{u3, u2} δ β _inst_4 _inst_2)) (fun (g : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => BoundedContinuousFunction.extend.{u1, u2, u3} α β _inst_1 _inst_2 δ _inst_4 _inst_5 f g h)
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : PseudoMetricSpace.{u3} β] {δ : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} δ] [_inst_5 : DiscreteTopology.{u1} δ _inst_4] (f : Function.Embedding.{succ u2, succ u1} α δ) (h : BoundedContinuousFunction.{u1, u3} δ β _inst_4 _inst_2), Isometry.{max u2 u3, max u1 u3} (BoundedContinuousFunction.{u2, u3} α β _inst_1 _inst_2) (BoundedContinuousFunction.{u1, u3} δ β _inst_4 _inst_2) (PseudoMetricSpace.toPseudoEMetricSpace.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α β _inst_1 _inst_2) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u2, u3} α β _inst_1 _inst_2)) (PseudoMetricSpace.toPseudoEMetricSpace.{max u3 u1} (BoundedContinuousFunction.{u1, u3} δ β _inst_4 _inst_2) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u1, u3} δ β _inst_4 _inst_2)) (fun (g : BoundedContinuousFunction.{u2, u3} α β _inst_1 _inst_2) => BoundedContinuousFunction.extend.{u2, u3, u1} α β _inst_1 _inst_2 δ _inst_4 _inst_5 f g h)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.isometry_extend BoundedContinuousFunction.isometry_extendₓ'. -/
 theorem isometry_extend (f : α ↪ δ) (h : δ →ᵇ β) : Isometry fun g : α →ᵇ β => extend f g h :=
   Isometry.of_dist_eq fun g₁ g₂ => by simp [dist_nonneg]
 #align bounded_continuous_function.isometry_extend BoundedContinuousFunction.isometry_extend
@@ -544,6 +858,12 @@ variable [TopologicalSpace α] [CompactSpace α] [PseudoMetricSpace β]
 
 variable {f g : α →ᵇ β} {x : α} {C : ℝ}
 
+/- warning: bounded_continuous_function.arzela_ascoli₁ -> BoundedContinuousFunction.arzela_ascoli₁ is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_3 : PseudoMetricSpace.{u2} β] [_inst_4 : CompactSpace.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3))] (A : Set.{max u2 u1} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)), (IsClosed.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3))) A) -> (Equicontinuous.{max u1 u2, u1, u2} (Set.Elem.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) A) α β _inst_1 (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3) (fun (x : Set.Elem.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) A) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) α (fun (a : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) a) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3)) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) α β _inst_1 _inst_3 (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3))) (Subtype.val.{max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (fun (x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (Set.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) (Set.instMembershipSet.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) x A) x))) -> (IsCompact.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3))) A)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.arzela_ascoli₁ BoundedContinuousFunction.arzela_ascoli₁ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y z «expr ∈ » U) -/
 /- Arzela-Ascoli theorem asserts that, on a compact space, a set of functions sharing
 a common modulus of continuity and taking values in a compact set forms a compact
@@ -616,6 +936,12 @@ theorem arzela_ascoli₁ [CompactSpace β] (A : Set (α →ᵇ β)) (closed : Is
       
 #align bounded_continuous_function.arzela_ascoli₁ BoundedContinuousFunction.arzela_ascoli₁
 
+/- warning: bounded_continuous_function.arzela_ascoli₂ -> BoundedContinuousFunction.arzela_ascoli₂ is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_3 : PseudoMetricSpace.{u2} β] (s : Set.{u2} β), (IsCompact.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3)) s) -> (forall (A : Set.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)), (IsClosed.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (BoundedContinuousFunction.pseudoMetricSpace.{u1, u2} α β _inst_1 _inst_3))) A) -> (forall (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (x : α), (Membership.Mem.{max u1 u2, max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (Set.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) (Set.hasMem.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) f A) -> (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_3) f x) s)) -> (Equicontinuous.{max u1 u2, u1, u2} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) A) α β _inst_1 (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) A) (fun (ᾰ : coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) A) => α -> β) (coeFnTrans.{max (succ u1) (succ u2), succ (max u1 u2), succ (max u1 u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) A) (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_3) (coeBaseAux.{succ (max u1 u2), succ (max u1 u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) A) (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (coeSubtype.{succ (max u1 u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (fun (x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) => Membership.Mem.{max u1 u2, max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (Set.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) (Set.hasMem.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) x A)))))) -> (IsCompact.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (BoundedContinuousFunction.pseudoMetricSpace.{u1, u2} α β _inst_1 _inst_3))) A))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_3 : PseudoMetricSpace.{u2} β] (s : Set.{u2} β), (IsCompact.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3)) s) -> (forall (A : Set.{max u2 u1} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)), (IsClosed.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3))) A) -> (forall (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (x : α), (Membership.mem.{max u1 u2, max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (Set.{max u2 u1} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) (Set.instMembershipSet.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) f A) -> (Membership.mem.{u2, u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (Set.{u2} β) (Set.instMembershipSet.{u2} β) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3)) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) α β _inst_1 _inst_3 (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3))) f x) s)) -> (Equicontinuous.{max u1 u2, u1, u2} (Set.Elem.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) A) α β _inst_1 (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3) (fun (x : Set.Elem.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) A) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) α (fun (a : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) a) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3)) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) α β _inst_1 _inst_3 (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3))) (Subtype.val.{max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (fun (x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (Set.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) (Set.instMembershipSet.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) x A) x))) -> (IsCompact.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3))) A))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.arzela_ascoli₂ BoundedContinuousFunction.arzela_ascoli₂ₓ'. -/
 /-- Second version, with pointwise equicontinuity and range in a compact subset -/
 theorem arzela_ascoli₂ (s : Set β) (hs : IsCompact s) (A : Set (α →ᵇ β)) (closed : IsClosed A)
     (in_s : ∀ (f : α →ᵇ β) (x : α), f ∈ A → f x ∈ s) (H : Equicontinuous (coeFn : A → α → β)) :
@@ -637,6 +963,12 @@ theorem arzela_ascoli₂ (s : Set β) (hs : IsCompact s) (A : Set (α →ᵇ β)
     exact ⟨g, hf, rfl⟩
 #align bounded_continuous_function.arzela_ascoli₂ BoundedContinuousFunction.arzela_ascoli₂
 
+/- warning: bounded_continuous_function.arzela_ascoli -> BoundedContinuousFunction.arzela_ascoli is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompactSpace.{u1} α _inst_1] [_inst_3 : PseudoMetricSpace.{u2} β] [_inst_4 : T2Space.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3))] (s : Set.{u2} β), (IsCompact.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3)) s) -> (forall (A : Set.{max u2 u1} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)), (forall (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (x : α), (Membership.mem.{max u1 u2, max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (Set.{max u2 u1} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) (Set.instMembershipSet.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) f A) -> (Membership.mem.{u2, u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (Set.{u2} β) (Set.instMembershipSet.{u2} β) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3)) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) α β _inst_1 _inst_3 (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3))) f x) s)) -> (Equicontinuous.{max u1 u2, u1, u2} (Set.Elem.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) A) α β _inst_1 (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3) (fun (x : Set.Elem.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) A) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) α (fun (a : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) a) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3)) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) α β _inst_1 _inst_3 (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3))) (Subtype.val.{max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (fun (x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) => Membership.mem.{max u1 u2, max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (Set.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) (Set.instMembershipSet.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3)) x A) x))) -> (IsCompact.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3))) (closure.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_3))) A)))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.arzela_ascoli BoundedContinuousFunction.arzela_ascoliₓ'. -/
 /-- Third (main) version, with pointwise equicontinuity and range in a compact subset, but
 without closedness. The closure is then compact -/
 theorem arzela_ascoli [T2Space β] (s : Set β) (hs : IsCompact s) (A : Set (α →ᵇ β))
@@ -663,30 +995,46 @@ variable [TopologicalSpace α] [PseudoMetricSpace β] [One β]
 instance : One (α →ᵇ β) :=
   ⟨const α 1⟩
 
+/- warning: bounded_continuous_function.coe_one -> BoundedContinuousFunction.coe_one is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_one BoundedContinuousFunction.coe_oneₓ'. -/
 @[simp, to_additive]
 theorem coe_one : ((1 : α →ᵇ β) : α → β) = 1 :=
   rfl
 #align bounded_continuous_function.coe_one BoundedContinuousFunction.coe_one
 #align bounded_continuous_function.coe_zero BoundedContinuousFunction.coe_zero
 
+#print BoundedContinuousFunction.mkOfCompact_one /-
 @[simp, to_additive]
 theorem mkOfCompact_one [CompactSpace α] : mkOfCompact (1 : C(α, β)) = 1 :=
   rfl
 #align bounded_continuous_function.mk_of_compact_one BoundedContinuousFunction.mkOfCompact_one
 #align bounded_continuous_function.mk_of_compact_zero BoundedContinuousFunction.mkOfCompact_zero
+-/
 
+/- warning: bounded_continuous_function.forall_coe_one_iff_one -> BoundedContinuousFunction.forall_coe_one_iff_one is a dubious translation:
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+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] [_inst_3 : One.{u2} β] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2), Iff (forall (x : α), Eq.{succ u2} β (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f x) (OfNat.ofNat.{u2} β 1 (OfNat.mk.{u2} β 1 (One.one.{u2} β _inst_3)))) (Eq.{succ (max u1 u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) f (OfNat.ofNat.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) 1 (OfNat.mk.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) 1 (One.one.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.hasOne.{u1, u2} α β _inst_1 _inst_2 _inst_3)))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.forall_coe_one_iff_one BoundedContinuousFunction.forall_coe_one_iff_oneₓ'. -/
 @[to_additive]
 theorem forall_coe_one_iff_one (f : α →ᵇ β) : (∀ x, f x = 1) ↔ f = 1 :=
   (@FunLike.ext_iff _ _ _ _ f 1).symm
 #align bounded_continuous_function.forall_coe_one_iff_one BoundedContinuousFunction.forall_coe_one_iff_one
 #align bounded_continuous_function.forall_coe_zero_iff_zero BoundedContinuousFunction.forall_coe_zero_iff_zero
 
+#print BoundedContinuousFunction.one_compContinuous /-
 @[simp, to_additive]
 theorem one_compContinuous [TopologicalSpace γ] (f : C(γ, α)) :
     (1 : α →ᵇ β).comp_continuous f = 1 :=
   rfl
 #align bounded_continuous_function.one_comp_continuous BoundedContinuousFunction.one_compContinuous
 #align bounded_continuous_function.zero_comp_continuous BoundedContinuousFunction.zero_compContinuous
+-/
 
 end One
 
@@ -722,43 +1070,87 @@ instance : Add (α →ᵇ β)
         exact Classical.choose_spec f.bounded x y
         exact Classical.choose_spec g.bounded x y)
 
+/- warning: bounded_continuous_function.coe_add -> BoundedContinuousFunction.coe_add is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_add BoundedContinuousFunction.coe_addₓ'. -/
 @[simp]
 theorem coe_add : ⇑(f + g) = f + g :=
   rfl
 #align bounded_continuous_function.coe_add BoundedContinuousFunction.coe_add
 
+/- warning: bounded_continuous_function.add_apply -> BoundedContinuousFunction.add_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.add_apply BoundedContinuousFunction.add_applyₓ'. -/
 theorem add_apply : (f + g) x = f x + g x :=
   rfl
 #align bounded_continuous_function.add_apply BoundedContinuousFunction.add_apply
 
+/- warning: bounded_continuous_function.mk_of_compact_add -> BoundedContinuousFunction.mkOfCompact_add is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.mk_of_compact_add BoundedContinuousFunction.mkOfCompact_addₓ'. -/
 @[simp]
 theorem mkOfCompact_add [CompactSpace α] (f g : C(α, β)) :
     mkOfCompact (f + g) = mkOfCompact f + mkOfCompact g :=
   rfl
 #align bounded_continuous_function.mk_of_compact_add BoundedContinuousFunction.mkOfCompact_add
 
+/- warning: bounded_continuous_function.add_comp_continuous -> BoundedContinuousFunction.add_compContinuous is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.add_comp_continuous BoundedContinuousFunction.add_compContinuousₓ'. -/
 theorem add_compContinuous [TopologicalSpace γ] (h : C(γ, α)) :
     (g + f).comp_continuous h = g.comp_continuous h + f.comp_continuous h :=
   rfl
 #align bounded_continuous_function.add_comp_continuous BoundedContinuousFunction.add_compContinuous
 
+/- warning: bounded_continuous_function.coe_nsmul_rec -> BoundedContinuousFunction.coe_nsmulRec is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_nsmul_rec BoundedContinuousFunction.coe_nsmulRecₓ'. -/
 @[simp]
 theorem coe_nsmulRec : ∀ n, ⇑(nsmulRec n f) = n • f
   | 0 => by rw [nsmulRec, zero_smul, coe_zero]
   | n + 1 => by rw [nsmulRec, succ_nsmul, coe_add, coe_nsmul_rec]
 #align bounded_continuous_function.coe_nsmul_rec BoundedContinuousFunction.coe_nsmulRec
 
+#print BoundedContinuousFunction.hasNatScalar /-
 instance hasNatScalar : SMul ℕ (α →ᵇ β)
     where smul n f :=
     { toContinuousMap := n • f.toContinuousMap
       map_bounded' := by simpa [coe_nsmul_rec] using (nsmulRec n f).map_bounded' }
 #align bounded_continuous_function.has_nat_scalar BoundedContinuousFunction.hasNatScalar
+-/
 
+/- warning: bounded_continuous_function.coe_nsmul -> BoundedContinuousFunction.coe_nsmul is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] [_inst_3 : AddMonoid.{u2} β] [_inst_4 : LipschitzAdd.{u2} β _inst_2 _inst_3] (r : Nat) (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2), Eq.{succ (max u1 u2)} (α -> β) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) (SMul.smul.{0, max u1 u2} Nat (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.hasNatScalar.{u1, u2} α β _inst_1 _inst_2 _inst_3 _inst_4) r f)) (SMul.smul.{0, max u1 u2} Nat (α -> β) (Function.hasSMul.{u1, 0, u2} α Nat β (AddMonoid.SMul.{u2} β _inst_3)) r (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_nsmul BoundedContinuousFunction.coe_nsmulₓ'. -/
 @[simp]
 theorem coe_nsmul (r : ℕ) (f : α →ᵇ β) : ⇑(r • f) = r • f :=
   rfl
 #align bounded_continuous_function.coe_nsmul BoundedContinuousFunction.coe_nsmul
 
+/- warning: bounded_continuous_function.nsmul_apply -> BoundedContinuousFunction.nsmul_apply is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] [_inst_3 : AddMonoid.{u2} β] [_inst_4 : LipschitzAdd.{u2} β _inst_2 _inst_3] (r : Nat) (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (v : α), Eq.{succ u2} β (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) (SMul.smul.{0, max u1 u2} Nat (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.hasNatScalar.{u1, u2} α β _inst_1 _inst_2 _inst_3 _inst_4) r f) v) (SMul.smul.{0, u2} Nat β (AddMonoid.SMul.{u2} β _inst_3) r (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f v))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.nsmul_apply BoundedContinuousFunction.nsmul_applyₓ'. -/
 @[simp]
 theorem nsmul_apply (r : ℕ) (f : α →ᵇ β) (v : α) : (r • f) v = r • f v :=
   rfl
@@ -779,6 +1171,7 @@ instance : LipschitzAdd (α →ᵇ β)
       refine' mul_le_mul_of_nonneg_left _ C_nonneg
       apply max_le_max <;> exact dist_coe_le_dist x⟩
 
+#print BoundedContinuousFunction.coeFnAddHom /-
 /-- Coercion of a `normed_add_group_hom` is an `add_monoid_hom`. Similar to
 `add_monoid_hom.coe_fn`. -/
 @[simps]
@@ -787,9 +1180,16 @@ def coeFnAddHom : (α →ᵇ β) →+ α → β where
   map_zero' := coe_zero
   map_add' := coe_add
 #align bounded_continuous_function.coe_fn_add_hom BoundedContinuousFunction.coeFnAddHom
+-/
 
 variable (α β)
 
+/- warning: bounded_continuous_function.to_continuous_map_add_hom -> BoundedContinuousFunction.toContinuousMapAddHom is a dubious translation:
+lean 3 declaration is
+  forall (α : Type.{u1}) (β : Type.{u2}) [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : PseudoMetricSpace.{u2} β] [_inst_3 : AddMonoid.{u2} β] [_inst_4 : LipschitzAdd.{u2} β _inst_2 _inst_3], AddMonoidHom.{max u1 u2, max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2))) (AddMonoid.toAddZeroClass.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.addMonoid.{u1, u2} α β _inst_1 _inst_2 _inst_3 _inst_4)) (ContinuousMap.addZeroClass.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_2)) (AddMonoid.toAddZeroClass.{u2} β _inst_3) (LipschitzAdd.continuousAdd.{u2} β _inst_2 _inst_3 _inst_4))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.to_continuous_map_add_hom BoundedContinuousFunction.toContinuousMapAddHomₓ'. -/
 /-- The additive map forgetting that a bounded continuous function is bounded.
 -/
 @[simps]
@@ -817,12 +1217,24 @@ instance : AddCommMonoid (α →ᵇ β) :=
 
 open BigOperators
 
+/- warning: bounded_continuous_function.coe_sum -> BoundedContinuousFunction.coe_sum is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_sum BoundedContinuousFunction.coe_sumₓ'. -/
 @[simp]
 theorem coe_sum {ι : Type _} (s : Finset ι) (f : ι → α →ᵇ β) :
     ⇑(∑ i in s, f i) = ∑ i in s, (f i : α → β) :=
   (@coeFnAddHom α β _ _ _ _).map_sum f s
 #align bounded_continuous_function.coe_sum BoundedContinuousFunction.coe_sum
 
+/- warning: bounded_continuous_function.sum_apply -> BoundedContinuousFunction.sum_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.sum_apply BoundedContinuousFunction.sum_applyₓ'. -/
 theorem sum_apply {ι : Type _} (s : Finset ι) (f : ι → α →ᵇ β) (a : α) :
     (∑ i in s, f i) a = ∑ i in s, f i a := by simp
 #align bounded_continuous_function.sum_apply BoundedContinuousFunction.sum_apply
@@ -841,16 +1253,34 @@ variable (f g : α →ᵇ β) {x : α} {C : ℝ}
 instance : Norm (α →ᵇ β) :=
   ⟨fun u => dist u 0⟩
 
+/- warning: bounded_continuous_function.norm_def -> BoundedContinuousFunction.norm_def is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.norm_def BoundedContinuousFunction.norm_defₓ'. -/
 theorem norm_def : ‖f‖ = dist f 0 :=
   rfl
 #align bounded_continuous_function.norm_def BoundedContinuousFunction.norm_def
 
+/- warning: bounded_continuous_function.norm_eq -> BoundedContinuousFunction.norm_eq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.norm_eq BoundedContinuousFunction.norm_eqₓ'. -/
 /-- The norm of a bounded continuous function is the supremum of `‖f x‖`.
 We use `Inf` to ensure that the definition works if `α` has no elements. -/
 theorem norm_eq (f : α →ᵇ β) : ‖f‖ = sInf { C : ℝ | 0 ≤ C ∧ ∀ x : α, ‖f x‖ ≤ C } := by
   simp [norm_def, BoundedContinuousFunction.dist_eq]
 #align bounded_continuous_function.norm_eq BoundedContinuousFunction.norm_eq
 
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.norm_eq_of_nonempty BoundedContinuousFunction.norm_eq_of_nonemptyₓ'. -/
 /-- When the domain is non-empty, we do not need the `0 ≤ C` condition in the formula for ‖f‖ as an
 `Inf`. -/
 theorem norm_eq_of_nonempty [h : Nonempty α] : ‖f‖ = sInf { C : ℝ | ∀ x : α, ‖f x‖ ≤ C } :=
@@ -863,11 +1293,23 @@ theorem norm_eq_of_nonempty [h : Nonempty α] : ‖f‖ = sInf { C : ℝ | ∀ x
   exact fun h' => le_trans (norm_nonneg (f a)) (h' a)
 #align bounded_continuous_function.norm_eq_of_nonempty BoundedContinuousFunction.norm_eq_of_nonempty
 
+/- warning: bounded_continuous_function.norm_eq_zero_of_empty -> BoundedContinuousFunction.norm_eq_zero_of_empty is a dubious translation:
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+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) [h : IsEmpty.{succ u1} α], Eq.{1} Real (Norm.norm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.hasNorm.{u1, u2} α β _inst_1 _inst_2) f) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.norm_eq_zero_of_empty BoundedContinuousFunction.norm_eq_zero_of_emptyₓ'. -/
 @[simp]
 theorem norm_eq_zero_of_empty [h : IsEmpty α] : ‖f‖ = 0 :=
   dist_zero_of_empty
 #align bounded_continuous_function.norm_eq_zero_of_empty BoundedContinuousFunction.norm_eq_zero_of_empty
 
+/- warning: bounded_continuous_function.norm_coe_le_norm -> BoundedContinuousFunction.norm_coe_le_norm is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.norm_coe_le_norm BoundedContinuousFunction.norm_coe_le_normₓ'. -/
 theorem norm_coe_le_norm (x : α) : ‖f x‖ ≤ ‖f‖ :=
   calc
     ‖f x‖ = dist (f x) ((0 : α →ᵇ β) x) := by simp [dist_zero_right]
@@ -875,6 +1317,12 @@ theorem norm_coe_le_norm (x : α) : ‖f x‖ ≤ ‖f‖ :=
     
 #align bounded_continuous_function.norm_coe_le_norm BoundedContinuousFunction.norm_coe_le_norm
 
+/- warning: bounded_continuous_function.dist_le_two_norm' -> BoundedContinuousFunction.dist_le_two_norm' is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.dist_le_two_norm' BoundedContinuousFunction.dist_le_two_norm'ₓ'. -/
 theorem dist_le_two_norm' {f : γ → β} {C : ℝ} (hC : ∀ x, ‖f x‖ ≤ C) (x y : γ) :
     dist (f x) (f y) ≤ 2 * C :=
   calc
@@ -884,6 +1332,12 @@ theorem dist_le_two_norm' {f : γ → β} {C : ℝ} (hC : ∀ x, ‖f x‖ ≤ C
     
 #align bounded_continuous_function.dist_le_two_norm' BoundedContinuousFunction.dist_le_two_norm'
 
+/- warning: bounded_continuous_function.dist_le_two_norm -> BoundedContinuousFunction.dist_le_two_norm is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.dist_le_two_norm BoundedContinuousFunction.dist_le_two_normₓ'. -/
 /-- Distance between the images of any two points is at most twice the norm of the function. -/
 theorem dist_le_two_norm (x y : α) : dist (f x) (f y) ≤ 2 * ‖f‖ :=
   dist_le_two_norm' f.norm_coe_le_norm x y
@@ -891,17 +1345,35 @@ theorem dist_le_two_norm (x y : α) : dist (f x) (f y) ≤ 2 * ‖f‖ :=
 
 variable {f}
 
+/- warning: bounded_continuous_function.norm_le -> BoundedContinuousFunction.norm_le is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.norm_le BoundedContinuousFunction.norm_leₓ'. -/
 /-- The norm of a function is controlled by the supremum of the pointwise norms -/
 theorem norm_le (C0 : (0 : ℝ) ≤ C) : ‖f‖ ≤ C ↔ ∀ x : α, ‖f x‖ ≤ C := by
   simpa using @dist_le _ _ _ _ f 0 _ C0
 #align bounded_continuous_function.norm_le BoundedContinuousFunction.norm_le
 
+/- warning: bounded_continuous_function.norm_le_of_nonempty -> BoundedContinuousFunction.norm_le_of_nonempty is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : Nonempty.{succ u1} α] {f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)} {M : Real}, Iff (LE.le.{0} Real Real.hasLe (Norm.norm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.hasNorm.{u1, u2} α β _inst_1 _inst_2) f) M) (forall (x : α), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} β (SeminormedAddCommGroup.toHasNorm.{u2} β _inst_2) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) f x)) M)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : Nonempty.{succ u1} α] {f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)} {M : Real}, Iff (LE.le.{0} Real Real.instLEReal (Norm.norm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.instNormBoundedContinuousFunctionToPseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2) f) M) (forall (x : α), LE.le.{0} Real Real.instLEReal (Norm.norm.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (SeminormedAddCommGroup.toNorm.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) f x)) M)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.norm_le_of_nonempty BoundedContinuousFunction.norm_le_of_nonemptyₓ'. -/
 theorem norm_le_of_nonempty [Nonempty α] {f : α →ᵇ β} {M : ℝ} : ‖f‖ ≤ M ↔ ∀ x, ‖f x‖ ≤ M :=
   by
   simp_rw [norm_def, ← dist_zero_right]
   exact dist_le_iff_of_nonempty
 #align bounded_continuous_function.norm_le_of_nonempty BoundedContinuousFunction.norm_le_of_nonempty
 
+/- warning: bounded_continuous_function.norm_lt_iff_of_compact -> BoundedContinuousFunction.norm_lt_iff_of_compact is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : CompactSpace.{u1} α _inst_1] {f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)} {M : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) M) -> (Iff (LT.lt.{0} Real Real.hasLt (Norm.norm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.hasNorm.{u1, u2} α β _inst_1 _inst_2) f) M) (forall (x : α), LT.lt.{0} Real Real.hasLt (Norm.norm.{u2} β (SeminormedAddCommGroup.toHasNorm.{u2} β _inst_2) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) f x)) M))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : CompactSpace.{u1} α _inst_1] {f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)} {M : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) M) -> (Iff (LT.lt.{0} Real Real.instLTReal (Norm.norm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.instNormBoundedContinuousFunctionToPseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2) f) M) (forall (x : α), LT.lt.{0} Real Real.instLTReal (Norm.norm.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (SeminormedAddCommGroup.toNorm.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) f x)) M))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.norm_lt_iff_of_compact BoundedContinuousFunction.norm_lt_iff_of_compactₓ'. -/
 theorem norm_lt_iff_of_compact [CompactSpace α] {f : α →ᵇ β} {M : ℝ} (M0 : 0 < M) :
     ‖f‖ < M ↔ ∀ x, ‖f x‖ < M :=
   by
@@ -909,6 +1381,12 @@ theorem norm_lt_iff_of_compact [CompactSpace α] {f : α →ᵇ β} {M : ℝ} (M
   exact dist_lt_iff_of_compact M0
 #align bounded_continuous_function.norm_lt_iff_of_compact BoundedContinuousFunction.norm_lt_iff_of_compact
 
+/- warning: bounded_continuous_function.norm_lt_iff_of_nonempty_compact -> BoundedContinuousFunction.norm_lt_iff_of_nonempty_compact is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : Nonempty.{succ u1} α] [_inst_4 : CompactSpace.{u1} α _inst_1] {f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)} {M : Real}, Iff (LT.lt.{0} Real Real.hasLt (Norm.norm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.hasNorm.{u1, u2} α β _inst_1 _inst_2) f) M) (forall (x : α), LT.lt.{0} Real Real.hasLt (Norm.norm.{u2} β (SeminormedAddCommGroup.toHasNorm.{u2} β _inst_2) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) f x)) M)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : Nonempty.{succ u1} α] [_inst_4 : CompactSpace.{u1} α _inst_1] {f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)} {M : Real}, Iff (LT.lt.{0} Real Real.instLTReal (Norm.norm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.instNormBoundedContinuousFunctionToPseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2) f) M) (forall (x : α), LT.lt.{0} Real Real.instLTReal (Norm.norm.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (SeminormedAddCommGroup.toNorm.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) f x)) M)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.norm_lt_iff_of_nonempty_compact BoundedContinuousFunction.norm_lt_iff_of_nonempty_compactₓ'. -/
 theorem norm_lt_iff_of_nonempty_compact [Nonempty α] [CompactSpace α] {f : α →ᵇ β} {M : ℝ} :
     ‖f‖ < M ↔ ∀ x, ‖f x‖ < M :=
   by
@@ -918,17 +1396,35 @@ theorem norm_lt_iff_of_nonempty_compact [Nonempty α] [CompactSpace α] {f : α
 
 variable (f)
 
+/- warning: bounded_continuous_function.norm_const_le -> BoundedContinuousFunction.norm_const_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] (b : β), LE.le.{0} Real Real.hasLe (Norm.norm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.hasNorm.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.const.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) b)) (Norm.norm.{u2} β (SeminormedAddCommGroup.toHasNorm.{u2} β _inst_2) b)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] (b : β), LE.le.{0} Real Real.instLEReal (Norm.norm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.instNormBoundedContinuousFunctionToPseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.const.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) b)) (Norm.norm.{u2} β (SeminormedAddCommGroup.toNorm.{u2} β _inst_2) b)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.norm_const_le BoundedContinuousFunction.norm_const_leₓ'. -/
 /-- Norm of `const α b` is less than or equal to `‖b‖`. If `α` is nonempty,
 then it is equal to `‖b‖`. -/
 theorem norm_const_le (b : β) : ‖const α b‖ ≤ ‖b‖ :=
   (norm_le (norm_nonneg b)).2 fun x => le_rfl
 #align bounded_continuous_function.norm_const_le BoundedContinuousFunction.norm_const_le
 
+/- warning: bounded_continuous_function.norm_const_eq -> BoundedContinuousFunction.norm_const_eq is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [h : Nonempty.{succ u1} α] (b : β), Eq.{1} Real (Norm.norm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.hasNorm.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.const.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) b)) (Norm.norm.{u2} β (SeminormedAddCommGroup.toHasNorm.{u2} β _inst_2) b)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [h : Nonempty.{succ u1} α] (b : β), Eq.{1} Real (Norm.norm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.instNormBoundedContinuousFunctionToPseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.const.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) b)) (Norm.norm.{u2} β (SeminormedAddCommGroup.toNorm.{u2} β _inst_2) b)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.norm_const_eq BoundedContinuousFunction.norm_const_eqₓ'. -/
 @[simp]
 theorem norm_const_eq [h : Nonempty α] (b : β) : ‖const α b‖ = ‖b‖ :=
   le_antisymm (norm_const_le b) <| h.elim fun x => (const α b).norm_coe_le_norm x
 #align bounded_continuous_function.norm_const_eq BoundedContinuousFunction.norm_const_eq
 
+/- warning: bounded_continuous_function.of_normed_add_comm_group -> BoundedContinuousFunction.ofNormedAddCommGroup is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_3 : TopologicalSpace.{u1} α] [_inst_4 : SeminormedAddCommGroup.{u2} β] (f : α -> β), (Continuous.{u1, u2} α β _inst_3 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4))) f) -> (forall (C : Real), (forall (x : α), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} β (SeminormedAddCommGroup.toHasNorm.{u2} β _inst_4) (f x)) C) -> (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_3 : TopologicalSpace.{u1} α] [_inst_4 : SeminormedAddCommGroup.{u2} β] (f : α -> β), (Continuous.{u1, u2} α β _inst_3 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4))) f) -> (forall (C : Real), (forall (x : α), LE.le.{0} Real Real.instLEReal (Norm.norm.{u2} β (SeminormedAddCommGroup.toNorm.{u2} β _inst_4) (f x)) C) -> (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.of_normed_add_comm_group BoundedContinuousFunction.ofNormedAddCommGroupₓ'. -/
 /-- Constructing a bounded continuous function from a uniformly bounded continuous
 function taking values in a normed group. -/
 def ofNormedAddCommGroup {α : Type u} {β : Type v} [TopologicalSpace α] [SeminormedAddCommGroup β]
@@ -936,6 +1432,12 @@ def ofNormedAddCommGroup {α : Type u} {β : Type v} [TopologicalSpace α] [Semi
   ⟨⟨fun n => f n, Hf⟩, ⟨_, dist_le_two_norm' H⟩⟩
 #align bounded_continuous_function.of_normed_add_comm_group BoundedContinuousFunction.ofNormedAddCommGroup
 
+/- warning: bounded_continuous_function.coe_of_normed_add_comm_group -> BoundedContinuousFunction.coe_ofNormedAddCommGroup is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_3 : TopologicalSpace.{u1} α] [_inst_4 : SeminormedAddCommGroup.{u2} β] (f : α -> β) (Hf : Continuous.{u1, u2} α β _inst_3 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4))) f) (C : Real) (H : forall (x : α), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} β (SeminormedAddCommGroup.toHasNorm.{u2} β _inst_4) (f x)) C), Eq.{max (succ u1) (succ u2)} ((fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) => α -> β) (BoundedContinuousFunction.ofNormedAddCommGroup.{u1, u2} α β _inst_3 _inst_4 f Hf C H)) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) (BoundedContinuousFunction.ofNormedAddCommGroup.{u1, u2} α β _inst_3 _inst_4 f Hf C H)) f
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_3 : TopologicalSpace.{u1} α] [_inst_4 : SeminormedAddCommGroup.{u2} β] (f : α -> β) (Hf : Continuous.{u1, u2} α β _inst_3 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4))) f) (C : Real) (H : forall (x : α), LE.le.{0} Real Real.instLEReal (Norm.norm.{u2} β (SeminormedAddCommGroup.toNorm.{u2} β _inst_4) (f x)) C), Eq.{max (succ u1) (succ u2)} (forall (a : α), (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) α β _inst_3 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4))) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)))) (BoundedContinuousFunction.ofNormedAddCommGroup.{u1, u2} α β _inst_3 _inst_4 f Hf C H)) f
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_of_normed_add_comm_group BoundedContinuousFunction.coe_ofNormedAddCommGroupₓ'. -/
 @[simp]
 theorem coe_ofNormedAddCommGroup {α : Type u} {β : Type v} [TopologicalSpace α]
     [SeminormedAddCommGroup β] (f : α → β) (Hf : Continuous f) (C : ℝ) (H : ∀ x, ‖f x‖ ≤ C) :
@@ -943,11 +1445,23 @@ theorem coe_ofNormedAddCommGroup {α : Type u} {β : Type v} [TopologicalSpace 
   rfl
 #align bounded_continuous_function.coe_of_normed_add_comm_group BoundedContinuousFunction.coe_ofNormedAddCommGroup
 
+/- warning: bounded_continuous_function.norm_of_normed_add_comm_group_le -> BoundedContinuousFunction.norm_ofNormedAddCommGroup_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] {f : α -> β} (hfc : Continuous.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) f) {C : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) C) -> (forall (hfC : forall (x : α), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} β (SeminormedAddCommGroup.toHasNorm.{u2} β _inst_2) (f x)) C), LE.le.{0} Real Real.hasLe (Norm.norm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.hasNorm.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.ofNormedAddCommGroup.{u1, u2} α β _inst_1 _inst_2 f hfc C hfC)) C)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] {f : α -> β} (hfc : Continuous.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) f) {C : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) C) -> (forall (hfC : forall (x : α), LE.le.{0} Real Real.instLEReal (Norm.norm.{u2} β (SeminormedAddCommGroup.toNorm.{u2} β _inst_2) (f x)) C), LE.le.{0} Real Real.instLEReal (Norm.norm.{max u2 u1} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.instNormBoundedContinuousFunctionToPseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2) (BoundedContinuousFunction.ofNormedAddCommGroup.{u1, u2} α β _inst_1 _inst_2 f hfc C hfC)) C)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.norm_of_normed_add_comm_group_le BoundedContinuousFunction.norm_ofNormedAddCommGroup_leₓ'. -/
 theorem norm_ofNormedAddCommGroup_le {f : α → β} (hfc : Continuous f) {C : ℝ} (hC : 0 ≤ C)
     (hfC : ∀ x, ‖f x‖ ≤ C) : ‖ofNormedAddCommGroup f hfc C hfC‖ ≤ C :=
   (norm_le hC).2 hfC
 #align bounded_continuous_function.norm_of_normed_add_comm_group_le BoundedContinuousFunction.norm_ofNormedAddCommGroup_le
 
+/- warning: bounded_continuous_function.of_normed_add_comm_group_discrete -> BoundedContinuousFunction.ofNormedAddCommGroupDiscrete is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_3 : TopologicalSpace.{u1} α] [_inst_4 : DiscreteTopology.{u1} α _inst_3] [_inst_5 : SeminormedAddCommGroup.{u2} β] (f : α -> β) (C : Real), (forall (x : α), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} β (SeminormedAddCommGroup.toHasNorm.{u2} β _inst_5) (f x)) C) -> (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_5))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_3 : TopologicalSpace.{u1} α] [_inst_4 : DiscreteTopology.{u1} α _inst_3] [_inst_5 : SeminormedAddCommGroup.{u2} β] (f : α -> β) (C : Real), (forall (x : α), LE.le.{0} Real Real.instLEReal (Norm.norm.{u2} β (SeminormedAddCommGroup.toNorm.{u2} β _inst_5) (f x)) C) -> (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_5))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.of_normed_add_comm_group_discrete BoundedContinuousFunction.ofNormedAddCommGroupDiscreteₓ'. -/
 /-- Constructing a bounded continuous function from a uniformly bounded
 function on a discrete space, taking values in a normed group -/
 def ofNormedAddCommGroupDiscrete {α : Type u} {β : Type v} [TopologicalSpace α] [DiscreteTopology α]
@@ -955,6 +1469,12 @@ def ofNormedAddCommGroupDiscrete {α : Type u} {β : Type v} [TopologicalSpace 
   ofNormedAddCommGroup f continuous_of_discreteTopology C H
 #align bounded_continuous_function.of_normed_add_comm_group_discrete BoundedContinuousFunction.ofNormedAddCommGroupDiscrete
 
+/- warning: bounded_continuous_function.coe_of_normed_add_comm_group_discrete -> BoundedContinuousFunction.coe_ofNormedAddCommGroupDiscrete is a dubious translation:
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+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_3 : TopologicalSpace.{u1} α] [_inst_4 : DiscreteTopology.{u1} α _inst_3] [_inst_5 : SeminormedAddCommGroup.{u2} β] (f : α -> β) (C : Real) (H : forall (x : α), LE.le.{0} Real Real.hasLe (Norm.norm.{u2} β (SeminormedAddCommGroup.toHasNorm.{u2} β _inst_5) (f x)) C), Eq.{max (succ u1) (succ u2)} ((fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_5)) => α -> β) (BoundedContinuousFunction.ofNormedAddCommGroupDiscrete.{u1, u2} α β _inst_3 _inst_4 _inst_5 f C H)) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_5)) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_5)) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_5)) (BoundedContinuousFunction.ofNormedAddCommGroupDiscrete.{u1, u2} α β _inst_3 _inst_4 _inst_5 f C H)) f
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+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_3 : TopologicalSpace.{u1} α] [_inst_4 : DiscreteTopology.{u1} α _inst_3] [_inst_5 : SeminormedAddCommGroup.{u2} β] (f : α -> β) (C : Real) (H : forall (x : α), LE.le.{0} Real Real.instLEReal (Norm.norm.{u2} β (SeminormedAddCommGroup.toNorm.{u2} β _inst_5) (f x)) C), Eq.{max (succ u1) (succ u2)} (forall (a : α), (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_5)) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_5)) α β _inst_3 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_5))) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_5)) α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_5) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_5)))) (BoundedContinuousFunction.ofNormedAddCommGroupDiscrete.{u1, u2} α β _inst_3 _inst_4 _inst_5 f C H)) f
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_of_normed_add_comm_group_discrete BoundedContinuousFunction.coe_ofNormedAddCommGroupDiscreteₓ'. -/
 @[simp]
 theorem coe_ofNormedAddCommGroupDiscrete {α : Type u} {β : Type v} [TopologicalSpace α]
     [DiscreteTopology α] [SeminormedAddCommGroup β] (f : α → β) (C : ℝ) (H : ∀ x, ‖f x‖ ≤ C) :
@@ -962,25 +1482,51 @@ theorem coe_ofNormedAddCommGroupDiscrete {α : Type u} {β : Type v} [Topologica
   rfl
 #align bounded_continuous_function.coe_of_normed_add_comm_group_discrete BoundedContinuousFunction.coe_ofNormedAddCommGroupDiscrete
 
+#print BoundedContinuousFunction.normComp /-
 /-- Taking the pointwise norm of a bounded continuous function with values in a
 `seminormed_add_comm_group` yields a bounded continuous function with values in ℝ. -/
 def normComp : α →ᵇ ℝ :=
   f.comp norm lipschitzWith_one_norm
 #align bounded_continuous_function.norm_comp BoundedContinuousFunction.normComp
+-/
 
+/- warning: bounded_continuous_function.coe_norm_comp -> BoundedContinuousFunction.coe_normComp is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_norm_comp BoundedContinuousFunction.coe_normCompₓ'. -/
 @[simp]
 theorem coe_normComp : (f.normComp : α → ℝ) = norm ∘ f :=
   rfl
 #align bounded_continuous_function.coe_norm_comp BoundedContinuousFunction.coe_normComp
 
+/- warning: bounded_continuous_function.norm_norm_comp -> BoundedContinuousFunction.norm_normComp is a dubious translation:
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+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)), Eq.{1} Real (Norm.norm.{u1} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) (BoundedContinuousFunction.hasNorm.{u1, 0} α Real _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing))))) (BoundedContinuousFunction.normComp.{u1, u2} α β _inst_1 _inst_2 f)) (Norm.norm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.hasNorm.{u1, u2} α β _inst_1 _inst_2) f)
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.norm_norm_comp BoundedContinuousFunction.norm_normCompₓ'. -/
 @[simp]
 theorem norm_normComp : ‖f.normComp‖ = ‖f‖ := by simp only [norm_eq, coe_norm_comp, norm_norm]
 #align bounded_continuous_function.norm_norm_comp BoundedContinuousFunction.norm_normComp
 
+/- warning: bounded_continuous_function.bdd_above_range_norm_comp -> BoundedContinuousFunction.bddAbove_range_norm_comp is a dubious translation:
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+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)), BddAbove.{0} Real Real.preorder (Set.range.{0, succ u1} Real α (Function.comp.{succ u1, succ u2, 1} α β Real (Norm.norm.{u2} β (SeminormedAddCommGroup.toHasNorm.{u2} β _inst_2)) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) f)))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.bdd_above_range_norm_comp BoundedContinuousFunction.bddAbove_range_norm_compₓ'. -/
 theorem bddAbove_range_norm_comp : BddAbove <| Set.range <| norm ∘ f :=
   (Real.bounded_iff_bddBelow_bddAbove.mp <| @bounded_range _ _ _ _ f.normComp).2
 #align bounded_continuous_function.bdd_above_range_norm_comp BoundedContinuousFunction.bddAbove_range_norm_comp
 
+/- warning: bounded_continuous_function.norm_eq_supr_norm -> BoundedContinuousFunction.norm_eq_iSup_norm is a dubious translation:
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+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)), Eq.{1} Real (Norm.norm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.hasNorm.{u1, u2} α β _inst_1 _inst_2) f) (iSup.{0, succ u1} Real Real.hasSup α (fun (x : α) => Norm.norm.{u2} β (SeminormedAddCommGroup.toHasNorm.{u2} β _inst_2) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) f x)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)), Eq.{1} Real (Norm.norm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.instNormBoundedContinuousFunctionToPseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2) f) (iSup.{0, succ u1} Real Real.instSupSetReal α (fun (x : α) => Norm.norm.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (SeminormedAddCommGroup.toNorm.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) f x)))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.norm_eq_supr_norm BoundedContinuousFunction.norm_eq_iSup_normₓ'. -/
 theorem norm_eq_iSup_norm : ‖f‖ = ⨆ x : α, ‖f x‖ := by
   simp_rw [norm_def, dist_eq_supr, coe_zero, Pi.zero_apply, dist_zero_right]
 #align bounded_continuous_function.norm_eq_supr_norm BoundedContinuousFunction.norm_eq_iSup_norm
@@ -1006,52 +1552,108 @@ instance : Sub (α →ᵇ β) :=
           (add_le_add (f.norm_coe_le_norm x) <|
             trans_rel_right _ (norm_neg _) (g.norm_coe_le_norm x))⟩
 
+/- warning: bounded_continuous_function.coe_neg -> BoundedContinuousFunction.coe_neg is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_neg BoundedContinuousFunction.coe_negₓ'. -/
 @[simp]
 theorem coe_neg : ⇑(-f) = -f :=
   rfl
 #align bounded_continuous_function.coe_neg BoundedContinuousFunction.coe_neg
 
+/- warning: bounded_continuous_function.neg_apply -> BoundedContinuousFunction.neg_apply is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.neg_apply BoundedContinuousFunction.neg_applyₓ'. -/
 theorem neg_apply : (-f) x = -f x :=
   rfl
 #align bounded_continuous_function.neg_apply BoundedContinuousFunction.neg_apply
 
+/- warning: bounded_continuous_function.coe_sub -> BoundedContinuousFunction.coe_sub is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_sub BoundedContinuousFunction.coe_subₓ'. -/
 @[simp]
 theorem coe_sub : ⇑(f - g) = f - g :=
   rfl
 #align bounded_continuous_function.coe_sub BoundedContinuousFunction.coe_sub
 
+/- warning: bounded_continuous_function.sub_apply -> BoundedContinuousFunction.sub_apply is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.sub_apply BoundedContinuousFunction.sub_applyₓ'. -/
 theorem sub_apply : (f - g) x = f x - g x :=
   rfl
 #align bounded_continuous_function.sub_apply BoundedContinuousFunction.sub_apply
 
+/- warning: bounded_continuous_function.mk_of_compact_neg -> BoundedContinuousFunction.mkOfCompact_neg is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.mk_of_compact_neg BoundedContinuousFunction.mkOfCompact_negₓ'. -/
 @[simp]
 theorem mkOfCompact_neg [CompactSpace α] (f : C(α, β)) : mkOfCompact (-f) = -mkOfCompact f :=
   rfl
 #align bounded_continuous_function.mk_of_compact_neg BoundedContinuousFunction.mkOfCompact_neg
 
+/- warning: bounded_continuous_function.mk_of_compact_sub -> BoundedContinuousFunction.mkOfCompact_sub is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : CompactSpace.{u1} α _inst_1] (f : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (g : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))), Eq.{succ (max u1 u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 (HSub.hSub.{max u1 u2, max u1 u2, max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (instHSub.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (ContinuousMap.hasSub.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (SubNegMonoid.toHasSub.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)))) (TopologicalAddGroup.to_continuousSub.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} β _inst_2)))) f g)) (HSub.hSub.{max u1 u2, max u1 u2, max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (instHSub.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.hasSub.{u1, u2} α β _inst_1 _inst_2)) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 f) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 g))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : CompactSpace.{u1} α _inst_1] (f : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (g : ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))), Eq.{max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 (HSub.hSub.{max u1 u2, max u1 u2, max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (instHSub.{max u1 u2} (ContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (ContinuousMap.instSubContinuousMap.{u1, u2} α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (SubNegMonoid.toSub.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)))) (TopologicalAddGroup.to_continuousSub.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} β _inst_2)))) f g)) (HSub.hSub.{max u1 u2, max u1 u2, max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (instHSub.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.instSubBoundedContinuousFunctionToPseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2)) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 f) (BoundedContinuousFunction.mkOfCompact.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) _inst_3 g))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.mk_of_compact_sub BoundedContinuousFunction.mkOfCompact_subₓ'. -/
 @[simp]
 theorem mkOfCompact_sub [CompactSpace α] (f g : C(α, β)) :
     mkOfCompact (f - g) = mkOfCompact f - mkOfCompact g :=
   rfl
 #align bounded_continuous_function.mk_of_compact_sub BoundedContinuousFunction.mkOfCompact_sub
 
+/- warning: bounded_continuous_function.coe_zsmul_rec -> BoundedContinuousFunction.coe_zsmulRec is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (z : Int), Eq.{succ (max u1 u2)} (α -> β) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (zsmulRec.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.hasZero.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2))))))) (BoundedContinuousFunction.hasAdd.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} β _inst_2)) (BoundedContinuousFunction.hasNeg.{u1, u2} α β _inst_1 _inst_2) z f)) (SMul.smul.{0, max u1 u2} Int (α -> β) (Function.hasSMul.{u1, 0, u2} α Int β (SubNegMonoid.SMulInt.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2))))) z (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) f))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (z : Int), Eq.{max (succ u1) (succ u2)} (forall (ᾰ : α), (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) ᾰ) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (zsmulRec.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.instZeroBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2))))))) (BoundedContinuousFunction.instAddBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} β _inst_2)) (BoundedContinuousFunction.instNegBoundedContinuousFunctionToPseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2) z f)) (HSMul.hSMul.{0, max u1 u2, max u1 u2} Int (forall (a : α), (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) a) (forall (ᾰ : α), (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) ᾰ) (instHSMul.{0, max u1 u2} Int (forall (a : α), (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) a) (SubNegMonoid.SMulInt.{max u1 u2} (forall (a : α), (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) a) (Pi.subNegMonoid.{u1, u2} α (fun (a : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) a) (fun (i : α) => AddGroup.toSubNegMonoid.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) i) (SeminormedAddGroup.toAddGroup.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) i) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) i) _inst_2)))))) z (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) f))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_zsmul_rec BoundedContinuousFunction.coe_zsmulRecₓ'. -/
 @[simp]
 theorem coe_zsmulRec : ∀ z, ⇑(zsmulRec z f) = z • f
   | Int.ofNat n => by rw [zsmulRec, Int.ofNat_eq_coe, coe_nsmul_rec, coe_nat_zsmul]
   | -[n+1] => by rw [zsmulRec, negSucc_zsmul, coe_neg, coe_nsmul_rec]
 #align bounded_continuous_function.coe_zsmul_rec BoundedContinuousFunction.coe_zsmulRec
 
+#print BoundedContinuousFunction.hasIntScalar /-
 instance hasIntScalar : SMul ℤ (α →ᵇ β)
     where smul n f :=
     { toContinuousMap := n • f.toContinuousMap
       map_bounded' := by simpa using (zsmulRec n f).map_bounded' }
 #align bounded_continuous_function.has_int_scalar BoundedContinuousFunction.hasIntScalar
+-/
 
+/- warning: bounded_continuous_function.coe_zsmul -> BoundedContinuousFunction.coe_zsmul is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] (r : Int) (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (α -> β) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SMul.smul.{0, max u1 u2} Int (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.hasIntScalar.{u1, u2} α β _inst_1 _inst_2) r f)) (SMul.smul.{0, max u1 u2} Int (α -> β) (Function.hasSMul.{u1, 0, u2} α Int β (SubNegMonoid.SMulInt.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2))))) r (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) f))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] (r : Int) (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)), Eq.{max (succ u1) (succ u2)} (forall (ᾰ : α), (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) ᾰ) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (HSMul.hSMul.{0, max u1 u2, max u1 u2} Int (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (instHSMul.{0, max u1 u2} Int (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.hasIntScalar.{u1, u2} α β _inst_1 _inst_2)) r f)) (HSMul.hSMul.{0, max u1 u2, max u1 u2} Int (forall (a : α), (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) a) (forall (ᾰ : α), (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) ᾰ) (instHSMul.{0, max u1 u2} Int (forall (a : α), (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) a) (SubNegMonoid.SMulInt.{max u1 u2} (forall (a : α), (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) a) (Pi.subNegMonoid.{u1, u2} α (fun (a : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) a) (fun (i : α) => AddGroup.toSubNegMonoid.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) i) (SeminormedAddGroup.toAddGroup.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) i) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) i) _inst_2)))))) r (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) f))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_zsmul BoundedContinuousFunction.coe_zsmulₓ'. -/
 @[simp]
 theorem coe_zsmul (r : ℤ) (f : α →ᵇ β) : ⇑(r • f) = r • f :=
   rfl
 #align bounded_continuous_function.coe_zsmul BoundedContinuousFunction.coe_zsmul
 
+/- warning: bounded_continuous_function.zsmul_apply -> BoundedContinuousFunction.zsmul_apply is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.zsmul_apply BoundedContinuousFunction.zsmul_applyₓ'. -/
 @[simp]
 theorem zsmul_apply (r : ℤ) (f : α →ᵇ β) (v : α) : (r • f) v = r • f v :=
   rfl
@@ -1067,46 +1669,102 @@ instance : SeminormedAddCommGroup (α →ᵇ β)
 instance {α β} [TopologicalSpace α] [NormedAddCommGroup β] : NormedAddCommGroup (α →ᵇ β) :=
   { BoundedContinuousFunction.seminormedAddCommGroup with }
 
+/- warning: bounded_continuous_function.nnnorm_def -> BoundedContinuousFunction.nnnorm_def is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.nnnorm_def BoundedContinuousFunction.nnnorm_defₓ'. -/
 theorem nnnorm_def : ‖f‖₊ = nndist f 0 :=
   rfl
 #align bounded_continuous_function.nnnorm_def BoundedContinuousFunction.nnnorm_def
 
+/- warning: bounded_continuous_function.nnnorm_coe_le_nnnorm -> BoundedContinuousFunction.nnnorm_coe_le_nnnorm is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (x : α), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{u2} β (SeminormedAddGroup.toNNNorm.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) f x)) (NNNorm.nnnorm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SeminormedAddGroup.toNNNorm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SeminormedAddCommGroup.toSeminormedAddGroup.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α β _inst_1 _inst_2))) f)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (x : α), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNNorm.nnnorm.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (SeminormedAddGroup.toNNNorm.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) f x)) (NNNorm.nnnorm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SeminormedAddGroup.toNNNorm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SeminormedAddCommGroup.toSeminormedAddGroup.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α β _inst_1 _inst_2))) f)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.nnnorm_coe_le_nnnorm BoundedContinuousFunction.nnnorm_coe_le_nnnormₓ'. -/
 theorem nnnorm_coe_le_nnnorm (x : α) : ‖f x‖₊ ≤ ‖f‖₊ :=
   norm_coe_le_norm _ _
 #align bounded_continuous_function.nnnorm_coe_le_nnnorm BoundedContinuousFunction.nnnorm_coe_le_nnnorm
 
+/- warning: bounded_continuous_function.nndist_le_two_nnnorm -> BoundedContinuousFunction.nndist_le_two_nnnorm is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.nndist_le_two_nnnorm BoundedContinuousFunction.nndist_le_two_nnnormₓ'. -/
 theorem nndist_le_two_nnnorm (x y : α) : nndist (f x) (f y) ≤ 2 * ‖f‖₊ :=
   dist_le_two_norm _ _ _
 #align bounded_continuous_function.nndist_le_two_nnnorm BoundedContinuousFunction.nndist_le_two_nnnorm
 
+/- warning: bounded_continuous_function.nnnorm_le -> BoundedContinuousFunction.nnnorm_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (C : NNReal), Iff (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SeminormedAddGroup.toNNNorm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SeminormedAddCommGroup.toSeminormedAddGroup.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α β _inst_1 _inst_2))) f) C) (forall (x : α), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{u2} β (SeminormedAddGroup.toNNNorm.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) f x)) C)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.nnnorm_le BoundedContinuousFunction.nnnorm_leₓ'. -/
 /-- The nnnorm of a function is controlled by the supremum of the pointwise nnnorms -/
 theorem nnnorm_le (C : ℝ≥0) : ‖f‖₊ ≤ C ↔ ∀ x : α, ‖f x‖₊ ≤ C :=
   norm_le C.Prop
 #align bounded_continuous_function.nnnorm_le BoundedContinuousFunction.nnnorm_le
 
+/- warning: bounded_continuous_function.nnnorm_const_le -> BoundedContinuousFunction.nnnorm_const_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] (b : β), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (NNNorm.nnnorm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SeminormedAddGroup.toNNNorm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SeminormedAddCommGroup.toSeminormedAddGroup.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α β _inst_1 _inst_2))) (BoundedContinuousFunction.const.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) b)) (NNNorm.nnnorm.{u2} β (SeminormedAddGroup.toNNNorm.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)) b)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] (b : β), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (NNNorm.nnnorm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SeminormedAddGroup.toNNNorm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SeminormedAddCommGroup.toSeminormedAddGroup.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α β _inst_1 _inst_2))) (BoundedContinuousFunction.const.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) b)) (NNNorm.nnnorm.{u2} β (SeminormedAddGroup.toNNNorm.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)) b)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.nnnorm_const_le BoundedContinuousFunction.nnnorm_const_leₓ'. -/
 theorem nnnorm_const_le (b : β) : ‖const α b‖₊ ≤ ‖b‖₊ :=
   norm_const_le _
 #align bounded_continuous_function.nnnorm_const_le BoundedContinuousFunction.nnnorm_const_le
 
+#print BoundedContinuousFunction.nnnorm_const_eq /-
 @[simp]
 theorem nnnorm_const_eq [h : Nonempty α] (b : β) : ‖const α b‖₊ = ‖b‖₊ :=
   Subtype.ext <| norm_const_eq _
 #align bounded_continuous_function.nnnorm_const_eq BoundedContinuousFunction.nnnorm_const_eq
+-/
 
+/- warning: bounded_continuous_function.nnnorm_eq_supr_nnnorm -> BoundedContinuousFunction.nnnorm_eq_iSup_nnnorm is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)), Eq.{1} NNReal (NNNorm.nnnorm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SeminormedAddGroup.toNNNorm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SeminormedAddCommGroup.toSeminormedAddGroup.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α β _inst_1 _inst_2))) f) (iSup.{0, succ u1} NNReal (ConditionallyCompleteLattice.toHasSup.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot))) α (fun (x : α) => NNNorm.nnnorm.{u2} β (SeminormedAddGroup.toNNNorm.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2)) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) f x)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)), Eq.{1} NNReal (NNNorm.nnnorm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SeminormedAddGroup.toNNNorm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (SeminormedAddCommGroup.toSeminormedAddGroup.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.seminormedAddCommGroup.{u1, u2} α β _inst_1 _inst_2))) f) (iSup.{0, succ u1} NNReal (ConditionallyCompleteLattice.toSupSet.{0} NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal))) α (fun (x : α) => NNNorm.nnnorm.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (SeminormedAddGroup.toNNNorm.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) f x)))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.nnnorm_eq_supr_nnnorm BoundedContinuousFunction.nnnorm_eq_iSup_nnnormₓ'. -/
 theorem nnnorm_eq_iSup_nnnorm : ‖f‖₊ = ⨆ x : α, ‖f x‖₊ :=
   Subtype.ext <| (norm_eq_iSup_norm f).trans <| by simp_rw [NNReal.coe_iSup, coe_nnnorm]
 #align bounded_continuous_function.nnnorm_eq_supr_nnnorm BoundedContinuousFunction.nnnorm_eq_iSup_nnnorm
 
+/- warning: bounded_continuous_function.abs_diff_coe_le_dist -> BoundedContinuousFunction.abs_diff_coe_le_dist is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (g : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) {x : α}, LE.le.{0} Real Real.hasLe (Norm.norm.{u2} β (SeminormedAddCommGroup.toHasNorm.{u2} β _inst_2) (HSub.hSub.{u2, u2, u2} β β β (instHSub.{u2} β (SubNegMonoid.toHasSub.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_2))))) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) f x) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) g x))) (Dist.dist.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.hasDist.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) f g)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (g : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) {x : α}, LE.le.{0} Real Real.instLEReal (Norm.norm.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (SeminormedAddCommGroup.toNorm.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) _inst_2) (HSub.hSub.{u2, u2, u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (instHSub.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (SubNegMonoid.toSub.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (AddGroup.toSubNegMonoid.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (SeminormedAddGroup.toAddGroup.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) _inst_2))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) g x))) (Dist.dist.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.instDistBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) f g)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.abs_diff_coe_le_dist BoundedContinuousFunction.abs_diff_coe_le_distₓ'. -/
 theorem abs_diff_coe_le_dist : ‖f x - g x‖ ≤ dist f g :=
   by
   rw [dist_eq_norm]
   exact (f - g).norm_coe_le_norm x
 #align bounded_continuous_function.abs_diff_coe_le_dist BoundedContinuousFunction.abs_diff_coe_le_dist
 
+/- warning: bounded_continuous_function.coe_le_coe_add_dist -> BoundedContinuousFunction.coe_le_coe_add_dist is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {f : BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace} {g : BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace}, LE.le.{0} Real Real.hasLe (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) => α -> Real) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) f x) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) => α -> Real) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) g x) (Dist.dist.{u1} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) (BoundedContinuousFunction.hasDist.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) f g))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {f : BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace} {g : BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace}, LE.le.{0} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => Real) x) Real.instLEReal (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) α Real _inst_1 Real.pseudoMetricSpace (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace))) f x) (HAdd.hAdd.{0, 0, 0} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => Real) x) Real ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => Real) x) (instHAdd.{0} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => Real) x) Real.instAddReal) (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) α Real _inst_1 Real.pseudoMetricSpace (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace))) g x) (Dist.dist.{u1} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) (BoundedContinuousFunction.instDistBoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) f g))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_le_coe_add_dist BoundedContinuousFunction.coe_le_coe_add_distₓ'. -/
 theorem coe_le_coe_add_dist {f g : α →ᵇ ℝ} : f x ≤ g x + dist f g :=
   sub_le_iff_le_add'.1 <| (abs_le.1 <| @dist_coe_le_dist _ _ _ _ f g x).2
 #align bounded_continuous_function.coe_le_coe_add_dist BoundedContinuousFunction.coe_le_coe_add_dist
 
+/- warning: bounded_continuous_function.norm_comp_continuous_le -> BoundedContinuousFunction.norm_compContinuous_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : TopologicalSpace.{u3} γ] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (g : ContinuousMap.{u3, u1} γ α _inst_3 _inst_1), LE.le.{0} Real Real.hasLe (Norm.norm.{max u3 u2} (BoundedContinuousFunction.{u3, u2} γ β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.hasNorm.{u3, u2} γ β _inst_3 _inst_2) (BoundedContinuousFunction.compContinuous.{u1, u2, u3} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) γ _inst_3 f g)) (Norm.norm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.hasNorm.{u1, u2} α β _inst_1 _inst_2) f)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : TopologicalSpace.{u3} γ] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (g : ContinuousMap.{u3, u1} γ α _inst_3 _inst_1), LE.le.{0} Real Real.instLEReal (Norm.norm.{max u2 u3} (BoundedContinuousFunction.{u3, u2} γ β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.instNormBoundedContinuousFunctionToPseudoMetricSpace.{u3, u2} γ β _inst_3 _inst_2) (BoundedContinuousFunction.compContinuous.{u1, u2, u3} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) γ _inst_3 f g)) (Norm.norm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.instNormBoundedContinuousFunctionToPseudoMetricSpace.{u1, u2} α β _inst_1 _inst_2) f)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.norm_comp_continuous_le BoundedContinuousFunction.norm_compContinuous_leₓ'. -/
 theorem norm_compContinuous_le [TopologicalSpace γ] (f : α →ᵇ β) (g : C(γ, α)) :
     ‖f.comp_continuous g‖ ≤ ‖f‖ :=
   ((lipschitz_compContinuous g).dist_le_mul f 0).trans <| by
@@ -1144,11 +1802,23 @@ instance : SMul 𝕜 (α →ᵇ β)
           refine' mul_le_mul_of_nonneg_left _ dist_nonneg
           exact hb x y⟩ }
 
+/- warning: bounded_continuous_function.coe_smul -> BoundedContinuousFunction.coe_smul is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {𝕜 : Type.{u3}} [_inst_1 : PseudoMetricSpace.{u3} 𝕜] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : PseudoMetricSpace.{u2} β] [_inst_4 : Zero.{u3} 𝕜] [_inst_5 : Zero.{u2} β] [_inst_6 : SMul.{u3, u2} 𝕜 β] [_inst_7 : BoundedSMul.{u3, u2} 𝕜 β _inst_1 _inst_3 _inst_4 _inst_5 _inst_6] (c : 𝕜) (f : BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3), Eq.{max (succ u1) (succ u2)} (α -> β) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_2 _inst_3) (SMul.smul.{u3, max u1 u2} 𝕜 (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (BoundedContinuousFunction.hasSmul.{u1, u2, u3} α β 𝕜 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) c f)) (fun (x : α) => SMul.smul.{u3, u2} 𝕜 β _inst_6 c (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_2 _inst_3) f x))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u3}} {𝕜 : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : PseudoMetricSpace.{u3} β] [_inst_4 : Zero.{u1} 𝕜] [_inst_5 : Zero.{u3} β] [_inst_6 : SMul.{u1, u3} 𝕜 β] [_inst_7 : BoundedSMul.{u1, u3} 𝕜 β _inst_1 _inst_3 _inst_4 _inst_5 _inst_6] (c : 𝕜) (f : BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3), Eq.{max (succ u2) (succ u3)} (forall (ᾰ : α), (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) ᾰ) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u2 u3, u2, u3} (BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) α β _inst_2 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β _inst_3)) (BoundedContinuousMapClass.toContinuousMapClass.{max u2 u3, u2, u3} (BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) α β _inst_2 _inst_3 (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3))) (HSMul.hSMul.{u1, max u2 u3, max u2 u3} 𝕜 (BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) (BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) (instHSMul.{u1, max u2 u3} 𝕜 (BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) (BoundedContinuousFunction.instSMulBoundedContinuousFunction.{u2, u3, u1} α β 𝕜 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7)) c f)) (fun (x : α) => HSMul.hSMul.{u1, u3, u3} 𝕜 ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (instHSMul.{u1, u3} 𝕜 ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) _inst_6) c (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u2 u3, u2, u3} (BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) α β _inst_2 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β _inst_3)) (BoundedContinuousMapClass.toContinuousMapClass.{max u2 u3, u2, u3} (BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) α β _inst_2 _inst_3 (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3))) f x))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_smul BoundedContinuousFunction.coe_smulₓ'. -/
 @[simp]
 theorem coe_smul (c : 𝕜) (f : α →ᵇ β) : ⇑(c • f) = fun x => c • f x :=
   rfl
 #align bounded_continuous_function.coe_smul BoundedContinuousFunction.coe_smul
 
+/- warning: bounded_continuous_function.smul_apply -> BoundedContinuousFunction.smul_apply is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {𝕜 : Type.{u3}} [_inst_1 : PseudoMetricSpace.{u3} 𝕜] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : PseudoMetricSpace.{u2} β] [_inst_4 : Zero.{u3} 𝕜] [_inst_5 : Zero.{u2} β] [_inst_6 : SMul.{u3, u2} 𝕜 β] [_inst_7 : BoundedSMul.{u3, u2} 𝕜 β _inst_1 _inst_3 _inst_4 _inst_5 _inst_6] (c : 𝕜) (f : BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (x : α), Eq.{succ u2} β (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_2 _inst_3) (SMul.smul.{u3, max u1 u2} 𝕜 (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (BoundedContinuousFunction.hasSmul.{u1, u2, u3} α β 𝕜 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) c f) x) (SMul.smul.{u3, u2} 𝕜 β _inst_6 c (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_2 _inst_3) f x))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u3}} {𝕜 : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : PseudoMetricSpace.{u3} β] [_inst_4 : Zero.{u1} 𝕜] [_inst_5 : Zero.{u3} β] [_inst_6 : SMul.{u1, u3} 𝕜 β] [_inst_7 : BoundedSMul.{u1, u3} 𝕜 β _inst_1 _inst_3 _inst_4 _inst_5 _inst_6] (c : 𝕜) (f : BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) (x : α), Eq.{succ u3} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u2 u3, u2, u3} (BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) α β _inst_2 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β _inst_3)) (BoundedContinuousMapClass.toContinuousMapClass.{max u2 u3, u2, u3} (BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) α β _inst_2 _inst_3 (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3))) (HSMul.hSMul.{u1, max u2 u3, max u2 u3} 𝕜 (BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) (BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) (instHSMul.{u1, max u2 u3} 𝕜 (BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) (BoundedContinuousFunction.instSMulBoundedContinuousFunction.{u2, u3, u1} α β 𝕜 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7)) c f) x) (HSMul.hSMul.{u1, u3, u3} 𝕜 ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (instHSMul.{u1, u3} 𝕜 ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) _inst_6) c (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u2 u3, u2, u3} (BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) α β _inst_2 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β _inst_3)) (BoundedContinuousMapClass.toContinuousMapClass.{max u2 u3, u2, u3} (BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) α β _inst_2 _inst_3 (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3))) f x))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.smul_apply BoundedContinuousFunction.smul_applyₓ'. -/
 theorem smul_apply (c : 𝕜) (f : α →ᵇ β) (x : α) : (c • f) x = c • f x :=
   rfl
 #align bounded_continuous_function.smul_apply BoundedContinuousFunction.smul_apply
@@ -1207,6 +1877,12 @@ instance : Module 𝕜 (α →ᵇ β) :=
 
 variable (𝕜)
 
+/- warning: bounded_continuous_function.eval_clm -> BoundedContinuousFunction.evalClm is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} (𝕜 : Type.{u3}) [_inst_1 : PseudoMetricSpace.{u3} 𝕜] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : PseudoMetricSpace.{u2} β] [_inst_4 : Semiring.{u3} 𝕜] [_inst_5 : AddCommMonoid.{u2} β] [_inst_6 : Module.{u3, u2} 𝕜 β _inst_4 _inst_5] [_inst_7 : BoundedSMul.{u3, u2} 𝕜 β _inst_1 _inst_3 (MulZeroClass.toHasZero.{u3} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 _inst_4)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5))) (SMulZeroClass.toHasSmul.{u3, u2} 𝕜 β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5))) (SMulWithZero.toSmulZeroClass.{u3, u2} 𝕜 β (MulZeroClass.toHasZero.{u3} 𝕜 (MulZeroOneClass.toMulZeroClass.{u3} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 _inst_4)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 β (Semiring.toMonoidWithZero.{u3} 𝕜 _inst_4) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5))) (Module.toMulActionWithZero.{u3, u2} 𝕜 β _inst_4 _inst_5 _inst_6))))] [_inst_8 : LipschitzAdd.{u2} β _inst_3 (AddCommMonoid.toAddMonoid.{u2} β _inst_5)], α -> (ContinuousLinearMap.{u3, u3, max u1 u2, u2} 𝕜 𝕜 _inst_4 _inst_4 (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 _inst_4)) (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (BoundedContinuousFunction.pseudoMetricSpace.{u1, u2} α β _inst_2 _inst_3))) (BoundedContinuousFunction.addAddCommMonoid.{u1, u2} α β _inst_2 _inst_3 _inst_5 _inst_8) β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3)) _inst_5 (BoundedContinuousFunction.module.{u1, u2, u3} α β 𝕜 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8) _inst_6)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} (𝕜 : Type.{u3}) [_inst_1 : PseudoMetricSpace.{u3} 𝕜] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : PseudoMetricSpace.{u2} β] [_inst_4 : Semiring.{u3} 𝕜] [_inst_5 : AddCommMonoid.{u2} β] [_inst_6 : Module.{u3, u2} 𝕜 β _inst_4 _inst_5] [_inst_7 : BoundedSMul.{u3, u2} 𝕜 β _inst_1 _inst_3 (MonoidWithZero.toZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 _inst_4)) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5)) (SMulZeroClass.toSMul.{u3, u2} 𝕜 β (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 β (MonoidWithZero.toZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 _inst_4)) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 β (Semiring.toMonoidWithZero.{u3} 𝕜 _inst_4) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5)) (Module.toMulActionWithZero.{u3, u2} 𝕜 β _inst_4 _inst_5 _inst_6))))] [_inst_8 : LipschitzAdd.{u2} β _inst_3 (AddCommMonoid.toAddMonoid.{u2} β _inst_5)], α -> (ContinuousLinearMap.{u3, u3, max u2 u1, u2} 𝕜 𝕜 _inst_4 _inst_4 (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 _inst_4)) (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3))) (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3 _inst_5 _inst_8) β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3)) _inst_5 (BoundedContinuousFunction.module.{u1, u2, u3} α β 𝕜 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8) _inst_6)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.eval_clm BoundedContinuousFunction.evalClmₓ'. -/
 /-- The evaluation at a point, as a continuous linear map from `α →ᵇ β` to `β`. -/
 def evalClm (x : α) : (α →ᵇ β) →L[𝕜] β where
   toFun f := f x
@@ -1214,6 +1890,12 @@ def evalClm (x : α) : (α →ᵇ β) →L[𝕜] β where
   map_smul' c f := smul_apply _ _ _
 #align bounded_continuous_function.eval_clm BoundedContinuousFunction.evalClm
 
+/- warning: bounded_continuous_function.eval_clm_apply -> BoundedContinuousFunction.evalClm_apply is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} (𝕜 : Type.{u3}) [_inst_1 : PseudoMetricSpace.{u3} 𝕜] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : PseudoMetricSpace.{u2} β] [_inst_4 : Semiring.{u3} 𝕜] [_inst_5 : AddCommMonoid.{u2} β] [_inst_6 : Module.{u3, u2} 𝕜 β _inst_4 _inst_5] [_inst_7 : BoundedSMul.{u3, u2} 𝕜 β _inst_1 _inst_3 (MulZeroClass.toHasZero.{u3} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 _inst_4)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5))) (SMulZeroClass.toHasSmul.{u3, u2} 𝕜 β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5))) (SMulWithZero.toSmulZeroClass.{u3, u2} 𝕜 β (MulZeroClass.toHasZero.{u3} 𝕜 (MulZeroOneClass.toMulZeroClass.{u3} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 _inst_4)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 β (Semiring.toMonoidWithZero.{u3} 𝕜 _inst_4) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5))) (Module.toMulActionWithZero.{u3, u2} 𝕜 β _inst_4 _inst_5 _inst_6))))] [_inst_8 : LipschitzAdd.{u2} β _inst_3 (AddCommMonoid.toAddMonoid.{u2} β _inst_5)] (x : α) (f : BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3), Eq.{succ u2} β (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ (max u1 u2)) (succ u2)} (ContinuousLinearMap.{u3, u3, max u1 u2, u2} 𝕜 𝕜 _inst_4 _inst_4 (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 _inst_4)) (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (BoundedContinuousFunction.pseudoMetricSpace.{u1, u2} α β _inst_2 _inst_3))) (BoundedContinuousFunction.addAddCommMonoid.{u1, u2} α β _inst_2 _inst_3 _inst_5 _inst_8) β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3)) _inst_5 (BoundedContinuousFunction.module.{u1, u2, u3} α β 𝕜 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8) _inst_6) (fun (_x : ContinuousLinearMap.{u3, u3, max u1 u2, u2} 𝕜 𝕜 _inst_4 _inst_4 (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 _inst_4)) (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (BoundedContinuousFunction.pseudoMetricSpace.{u1, u2} α β _inst_2 _inst_3))) (BoundedContinuousFunction.addAddCommMonoid.{u1, u2} α β _inst_2 _inst_3 _inst_5 _inst_8) β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3)) _inst_5 (BoundedContinuousFunction.module.{u1, u2, u3} α β 𝕜 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8) _inst_6) => (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) -> β) (ContinuousLinearMap.toFun.{u3, u3, max u1 u2, u2} 𝕜 𝕜 _inst_4 _inst_4 (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 _inst_4)) (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (BoundedContinuousFunction.pseudoMetricSpace.{u1, u2} α β _inst_2 _inst_3))) (BoundedContinuousFunction.addAddCommMonoid.{u1, u2} α β _inst_2 _inst_3 _inst_5 _inst_8) β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3)) _inst_5 (BoundedContinuousFunction.module.{u1, u2, u3} α β 𝕜 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8) _inst_6) (BoundedContinuousFunction.evalClm.{u1, u2, u3} α β 𝕜 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 x) f) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_2 _inst_3) f x)
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u3}} (𝕜 : Type.{u1}) [_inst_1 : PseudoMetricSpace.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : PseudoMetricSpace.{u3} β] [_inst_4 : Semiring.{u1} 𝕜] [_inst_5 : AddCommMonoid.{u3} β] [_inst_6 : Module.{u1, u3} 𝕜 β _inst_4 _inst_5] [_inst_7 : BoundedSMul.{u1, u3} 𝕜 β _inst_1 _inst_3 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 _inst_4)) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β _inst_5)) (SMulZeroClass.toSMul.{u1, u3} 𝕜 β (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, u3} 𝕜 β (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 _inst_4)) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 _inst_4) (AddMonoid.toZero.{u3} β (AddCommMonoid.toAddMonoid.{u3} β _inst_5)) (Module.toMulActionWithZero.{u1, u3} 𝕜 β _inst_4 _inst_5 _inst_6))))] [_inst_8 : LipschitzAdd.{u3} β _inst_3 (AddCommMonoid.toAddMonoid.{u3} β _inst_5)] (x : α) (f : BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3), Eq.{succ u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) => β) f) (FunLike.coe.{max (succ u2) (succ u3), max (succ u2) (succ u3), succ u3} (ContinuousLinearMap.{u1, u1, max u3 u2, u3} 𝕜 𝕜 _inst_4 _inst_4 (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 _inst_4)) (BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) (UniformSpace.toTopologicalSpace.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) (PseudoMetricSpace.toUniformSpace.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3))) (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u2, u3} α β _inst_2 _inst_3 _inst_5 _inst_8) β 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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.eval_clm_apply BoundedContinuousFunction.evalClm_applyₓ'. -/
 @[simp]
 theorem evalClm_apply (x : α) (f : α →ᵇ β) : evalClm 𝕜 x f = f x :=
   rfl
@@ -1221,6 +1903,12 @@ theorem evalClm_apply (x : α) (f : α →ᵇ β) : evalClm 𝕜 x f = f x :=
 
 variable (α β)
 
+/- warning: bounded_continuous_function.to_continuous_map_linear_map -> BoundedContinuousFunction.toContinuousMapLinearMap is a dubious translation:
+lean 3 declaration is
+  forall (α : Type.{u1}) (β : Type.{u2}) (𝕜 : Type.{u3}) [_inst_1 : PseudoMetricSpace.{u3} 𝕜] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : PseudoMetricSpace.{u2} β] [_inst_4 : Semiring.{u3} 𝕜] [_inst_5 : AddCommMonoid.{u2} β] [_inst_6 : Module.{u3, u2} 𝕜 β _inst_4 _inst_5] [_inst_7 : BoundedSMul.{u3, u2} 𝕜 β _inst_1 _inst_3 (MulZeroClass.toHasZero.{u3} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 _inst_4)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5))) (SMulZeroClass.toHasSmul.{u3, u2} 𝕜 β (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5))) (SMulWithZero.toSmulZeroClass.{u3, u2} 𝕜 β (MulZeroClass.toHasZero.{u3} 𝕜 (MulZeroOneClass.toMulZeroClass.{u3} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 _inst_4)))) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 β (Semiring.toMonoidWithZero.{u3} 𝕜 _inst_4) (AddZeroClass.toHasZero.{u2} β (AddMonoid.toAddZeroClass.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5))) (Module.toMulActionWithZero.{u3, u2} 𝕜 β _inst_4 _inst_5 _inst_6))))] [_inst_8 : LipschitzAdd.{u2} β _inst_3 (AddCommMonoid.toAddMonoid.{u2} β _inst_5)], LinearMap.{u3, u3, max u1 u2, max u1 u2} 𝕜 𝕜 _inst_4 _inst_4 (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 _inst_4)) (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (ContinuousMap.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3))) (BoundedContinuousFunction.addAddCommMonoid.{u1, u2} α β _inst_2 _inst_3 _inst_5 _inst_8) (ContinuousMap.addCommMonoid.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3)) _inst_5 (BoundedContinuousFunction.toContinuousMapLinearMap._proof_1.{u2} β _inst_3 _inst_5 _inst_8)) (BoundedContinuousFunction.module.{u1, u2, u3} α β 𝕜 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8) (ContinuousMap.module.{u1, u3, u2} α _inst_2 𝕜 β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3)) _inst_4 _inst_5 (BoundedContinuousFunction.toContinuousMapLinearMap._proof_2.{u2} β _inst_3 _inst_5 _inst_8) _inst_6 (BoundedContinuousFunction.toContinuousMapLinearMap._proof_3.{u3, u2} β 𝕜 _inst_1 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7))
+but is expected to have type
+  forall (α : Type.{u1}) (β : Type.{u2}) (𝕜 : Type.{u3}) [_inst_1 : PseudoMetricSpace.{u3} 𝕜] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : PseudoMetricSpace.{u2} β] [_inst_4 : Semiring.{u3} 𝕜] [_inst_5 : AddCommMonoid.{u2} β] [_inst_6 : Module.{u3, u2} 𝕜 β _inst_4 _inst_5] [_inst_7 : BoundedSMul.{u3, u2} 𝕜 β _inst_1 _inst_3 (MonoidWithZero.toZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 _inst_4)) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5)) (SMulZeroClass.toSMul.{u3, u2} 𝕜 β (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 β (MonoidWithZero.toZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 _inst_4)) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 β (Semiring.toMonoidWithZero.{u3} 𝕜 _inst_4) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5)) (Module.toMulActionWithZero.{u3, u2} 𝕜 β _inst_4 _inst_5 _inst_6))))] [_inst_8 : LipschitzAdd.{u2} β _inst_3 (AddCommMonoid.toAddMonoid.{u2} β _inst_5)], LinearMap.{u3, u3, max u2 u1, max u2 u1} 𝕜 𝕜 _inst_4 _inst_4 (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 _inst_4)) (BoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3) (ContinuousMap.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3))) (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, u2} α β _inst_2 _inst_3 _inst_5 _inst_8) (ContinuousMap.instAddCommMonoidContinuousMap.{u1, u2} α β _inst_2 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3)) _inst_5 (LipschitzAdd.continuousAdd.{u2} β _inst_3 (AddCommMonoid.toAddMonoid.{u2} β _inst_5) _inst_8)) (BoundedContinuousFunction.module.{u1, u2, u3} α β 𝕜 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8) (ContinuousMap.module.{u1, u3, u2} α _inst_2 𝕜 β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3)) _inst_4 _inst_5 (LipschitzAdd.continuousAdd.{u2} β _inst_3 (AddCommMonoid.toAddMonoid.{u2} β _inst_5) _inst_8) _inst_6 (ContinuousSMul.continuousConstSMul.{u3, u2} 𝕜 β (UniformSpace.toTopologicalSpace.{u3} 𝕜 (PseudoMetricSpace.toUniformSpace.{u3} 𝕜 _inst_1)) (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β _inst_3)) (SMulZeroClass.toSMul.{u3, u2} 𝕜 β (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 β (MonoidWithZero.toZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 _inst_4)) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 β (Semiring.toMonoidWithZero.{u3} 𝕜 _inst_4) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5)) (Module.toMulActionWithZero.{u3, u2} 𝕜 β _inst_4 _inst_5 _inst_6)))) (BoundedSMul.continuousSMul.{u3, u2} 𝕜 β _inst_1 _inst_3 (MonoidWithZero.toZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 _inst_4)) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5)) (SMulZeroClass.toSMul.{u3, u2} 𝕜 β (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5)) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 β (MonoidWithZero.toZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 _inst_4)) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5)) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 β (Semiring.toMonoidWithZero.{u3} 𝕜 _inst_4) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β _inst_5)) (Module.toMulActionWithZero.{u3, u2} 𝕜 β _inst_4 _inst_5 _inst_6)))) _inst_7)))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.to_continuous_map_linear_map BoundedContinuousFunction.toContinuousMapLinearMapₓ'. -/
 /-- The linear map forgetting that a bounded continuous function is bounded. -/
 @[simps]
 def toContinuousMapLinearMap : (α →ᵇ β) →ₗ[𝕜] C(α, β)
@@ -1264,6 +1952,12 @@ variable [SeminormedAddCommGroup γ] [NormedSpace 𝕜 γ]
 
 variable (α)
 
+/- warning: continuous_linear_map.comp_left_continuous_bounded -> ContinuousLinearMap.compLeftContinuousBounded is a dubious translation:
+lean 3 declaration is
+  forall (α : Type.{u1}) {β : Type.{u2}} {γ : Type.{u3}} {𝕜 : Type.{u4}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : NontriviallyNormedField.{u4} 𝕜] [_inst_4 : NormedSpace.{u4, u2} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_2] [_inst_5 : SeminormedAddCommGroup.{u3} γ] [_inst_6 : NormedSpace.{u4, u3} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_5], (ContinuousLinearMap.{u4, u4, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u4} 𝕜 (NormedRing.toRing.{u4} 𝕜 (NormedCommRing.toNormedRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜 (NormedRing.toRing.{u4} 𝕜 (NormedCommRing.toNormedRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (Ring.toSemiring.{u4} 𝕜 (NormedRing.toRing.{u4} 𝕜 (NormedCommRing.toNormedRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) γ (UniformSpace.toTopologicalSpace.{u3} γ (PseudoMetricSpace.toUniformSpace.{u3} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5))) (AddCommGroup.toAddCommMonoid.{u3} γ (SeminormedAddCommGroup.toAddCommGroup.{u3} γ _inst_5)) (NormedSpace.toModule.{u4, u2} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_2 _inst_4) (NormedSpace.toModule.{u4, u3} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_5 _inst_6)) -> (ContinuousLinearMap.{u4, u4, max u1 u2, max u1 u3} 𝕜 𝕜 (Ring.toSemiring.{u4} 𝕜 (NormedRing.toRing.{u4} 𝕜 (NormedCommRing.toNormedRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜 (NormedRing.toRing.{u4} 𝕜 (NormedCommRing.toNormedRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (Ring.toSemiring.{u4} 𝕜 (NormedRing.toRing.{u4} 𝕜 (NormedCommRing.toNormedRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.pseudoMetricSpace.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (BoundedContinuousFunction.addAddCommMonoid.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} β _inst_2)) (BoundedContinuousFunction.{u1, u3} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5)) (UniformSpace.toTopologicalSpace.{max u1 u3} (BoundedContinuousFunction.{u1, u3} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5)) (PseudoMetricSpace.toUniformSpace.{max u1 u3} (BoundedContinuousFunction.{u1, u3} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5)) (BoundedContinuousFunction.pseudoMetricSpace.{u1, u3} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5)))) (BoundedContinuousFunction.addAddCommMonoid.{u1, u3} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5) (AddCommGroup.toAddCommMonoid.{u3} γ (SeminormedAddCommGroup.toAddCommGroup.{u3} γ _inst_5)) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} γ _inst_5)) (BoundedContinuousFunction.module.{u1, u2, u4} α β 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (Ring.toSemiring.{u4} 𝕜 (NormedRing.toRing.{u4} 𝕜 (NormedCommRing.toNormedRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) (NormedSpace.toModule.{u4, u2} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_2 _inst_4) (ContinuousLinearMap.compLeftContinuousBounded._proof_1.{u4, u2} β 𝕜 _inst_2 _inst_3 _inst_4) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} β _inst_2)) (BoundedContinuousFunction.module.{u1, u3, u4} α γ 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5) (Ring.toSemiring.{u4} 𝕜 (NormedRing.toRing.{u4} 𝕜 (NormedCommRing.toNormedRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} γ (SeminormedAddCommGroup.toAddCommGroup.{u3} γ _inst_5)) (NormedSpace.toModule.{u4, u3} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_5 _inst_6) (ContinuousLinearMap.compLeftContinuousBounded._proof_2.{u4, u3} γ 𝕜 _inst_3 _inst_5 _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} γ _inst_5)))
+but is expected to have type
+  forall (α : Type.{u1}) {β : Type.{u2}} {γ : Type.{u3}} {𝕜 : Type.{u4}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : NontriviallyNormedField.{u4} 𝕜] [_inst_4 : NormedSpace.{u4, u2} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_2] [_inst_5 : SeminormedAddCommGroup.{u3} γ] [_inst_6 : NormedSpace.{u4, u3} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_5], (ContinuousLinearMap.{u4, u4, u2, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) γ (UniformSpace.toTopologicalSpace.{u3} γ (PseudoMetricSpace.toUniformSpace.{u3} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5))) (AddCommGroup.toAddCommMonoid.{u3} γ (SeminormedAddCommGroup.toAddCommGroup.{u3} γ _inst_5)) (NormedSpace.toModule.{u4, u2} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_2 _inst_4) (NormedSpace.toModule.{u4, u3} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_5 _inst_6)) -> (ContinuousLinearMap.{u4, u4, max u2 u1, max u3 u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))))) (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (UniformSpace.toTopologicalSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (PseudoMetricSpace.toUniformSpace.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2)))) (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} β _inst_2)) (BoundedContinuousFunction.{u1, u3} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5)) (UniformSpace.toTopologicalSpace.{max u1 u3} (BoundedContinuousFunction.{u1, u3} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5)) (PseudoMetricSpace.toUniformSpace.{max u1 u3} (BoundedContinuousFunction.{u1, u3} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5)) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u1, u3} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5)))) (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, u3} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5) (AddCommGroup.toAddCommMonoid.{u3} γ (SeminormedAddCommGroup.toAddCommGroup.{u3} γ _inst_5)) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} γ _inst_5)) (BoundedContinuousFunction.module.{u1, u2, u4} α β 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) (NormedSpace.toModule.{u4, u2} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_2 _inst_4) (NormedSpace.boundedSMul.{u4, u2} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_2 _inst_4) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} β _inst_2)) (BoundedContinuousFunction.module.{u1, u3, u4} α γ 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSeminormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5) (DivisionSemiring.toSemiring.{u4} 𝕜 (Semifield.toDivisionSemiring.{u4} 𝕜 (Field.toSemifield.{u4} 𝕜 (NormedField.toField.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} γ (SeminormedAddCommGroup.toAddCommGroup.{u3} γ _inst_5)) (NormedSpace.toModule.{u4, u3} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_5 _inst_6) (NormedSpace.boundedSMul.{u4, u3} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_5 _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} γ _inst_5)))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_left_continuous_bounded ContinuousLinearMap.compLeftContinuousBoundedₓ'. -/
 -- TODO does this work in the `has_bounded_smul` setting, too?
 /--
 Postcomposition of bounded continuous functions into a normed module by a continuous linear map is
@@ -1281,6 +1975,12 @@ protected def ContinuousLinearMap.compLeftContinuousBounded (g : β →L[𝕜] 
     norm_ofNormedAddCommGroup_le _ (mul_nonneg (norm_nonneg g) (norm_nonneg f)) _
 #align continuous_linear_map.comp_left_continuous_bounded ContinuousLinearMap.compLeftContinuousBounded
 
+/- warning: continuous_linear_map.comp_left_continuous_bounded_apply -> ContinuousLinearMap.compLeftContinuousBounded_apply is a dubious translation:
+lean 3 declaration is
+  forall (α : Type.{u1}) {β : Type.{u2}} {γ : Type.{u3}} {𝕜 : Type.{u4}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : SeminormedAddCommGroup.{u2} β] [_inst_3 : NontriviallyNormedField.{u4} 𝕜] [_inst_4 : NormedSpace.{u4, u2} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_2] [_inst_5 : SeminormedAddCommGroup.{u3} γ] [_inst_6 : NormedSpace.{u4, u3} 𝕜 γ (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) _inst_5] (g : ContinuousLinearMap.{u4, u4, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u4} 𝕜 (NormedRing.toRing.{u4} 𝕜 (NormedCommRing.toNormedRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (Ring.toSemiring.{u4} 𝕜 (NormedRing.toRing.{u4} 𝕜 (NormedCommRing.toNormedRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (RingHom.id.{u4} 𝕜 (Semiring.toNonAssocSemiring.{u4} 𝕜 (Ring.toSemiring.{u4} 𝕜 (NormedRing.toRing.{u4} 𝕜 (NormedCommRing.toNormedRing.{u4} 𝕜 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_inst_5)))) (BoundedContinuousFunction.addAddCommMonoid.{u1, u3} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} γ _inst_5) (AddCommGroup.toAddCommMonoid.{u3} γ (SeminormedAddCommGroup.toAddCommGroup.{u3} γ _inst_5)) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} γ _inst_5)) (BoundedContinuousFunction.module.{u1, u2, u4} α β 𝕜 (SeminormedRing.toPseudoMetricSpace.{u4} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u4} 𝕜 (NormedCommRing.toSeminormedCommRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_2) (Ring.toSemiring.{u4} 𝕜 (NormedRing.toRing.{u4} 𝕜 (NormedCommRing.toNormedRing.{u4} 𝕜 (NormedField.toNormedCommRing.{u4} 𝕜 (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_2)) (NormedSpace.toModule.{u4, u2} 𝕜 β (NontriviallyNormedField.toNormedField.{u4} 𝕜 _inst_3) 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+but is expected to have type
+  forall (α : Type.{u2}) {β : Type.{u3}} {γ : Type.{u4}} {𝕜 : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : SeminormedAddCommGroup.{u3} β] [_inst_3 : NontriviallyNormedField.{u1} 𝕜] [_inst_4 : NormedSpace.{u1, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3) _inst_2] [_inst_5 : SeminormedAddCommGroup.{u4} γ] [_inst_6 : NormedSpace.{u1, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3) _inst_5] (g : ContinuousLinearMap.{u1, u1, u3, u4} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 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(BoundedContinuousFunction.{u2, u3} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2)) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u2, u3} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2)))) (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u2, u3} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2) (AddCommGroup.toAddCommMonoid.{u3} β (SeminormedAddCommGroup.toAddCommGroup.{u3} β _inst_2)) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} β _inst_2)) (BoundedContinuousFunction.{u2, u4} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ _inst_5)) (UniformSpace.toTopologicalSpace.{max u2 u4} (BoundedContinuousFunction.{u2, u4} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ _inst_5)) (PseudoMetricSpace.toUniformSpace.{max u2 u4} (BoundedContinuousFunction.{u2, u4} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ _inst_5)) 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u4} (BoundedContinuousFunction.{u2, u4} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ _inst_5)) (PseudoMetricSpace.toUniformSpace.{max u2 u4} (BoundedContinuousFunction.{u2, u4} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ _inst_5)) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u2, u4} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ _inst_5)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max (max u2 u3) u4, u1, u1, max u2 u3, max u2 u4} (ContinuousLinearMap.{u1, u1, max u3 u2, max u4 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))))) (BoundedContinuousFunction.{u2, u3} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2)) (UniformSpace.toTopologicalSpace.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2)) (PseudoMetricSpace.toUniformSpace.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2)) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u2, u3} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2)))) (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u2, u3} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2) (AddCommGroup.toAddCommMonoid.{u3} β (SeminormedAddCommGroup.toAddCommGroup.{u3} β _inst_2)) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} β _inst_2)) (BoundedContinuousFunction.{u2, u4} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ _inst_5)) (UniformSpace.toTopologicalSpace.{max u2 u4} (BoundedContinuousFunction.{u2, u4} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ _inst_5)) (PseudoMetricSpace.toUniformSpace.{max u2 u4} (BoundedContinuousFunction.{u2, u4} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ _inst_5)) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u2, u4} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ _inst_5)))) (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u2, u4} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ _inst_5) (AddCommGroup.toAddCommMonoid.{u4} γ (SeminormedAddCommGroup.toAddCommGroup.{u4} γ _inst_5)) (SeminormedAddCommGroup.to_lipschitzAdd.{u4} γ _inst_5)) (BoundedContinuousFunction.module.{u2, u3, u1} α β 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (SeminormedAddCommGroup.toAddCommGroup.{u3} β _inst_2)) (NormedSpace.toModule.{u1, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3) _inst_2 _inst_4) (NormedSpace.boundedSMul.{u1, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3) _inst_2 _inst_4) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} β _inst_2)) (BoundedContinuousFunction.module.{u2, u4, u1} α γ 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ _inst_5) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (SeminormedAddCommGroup.toAddCommGroup.{u4} γ _inst_5)) (NormedSpace.toModule.{u1, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3) _inst_5 _inst_6) (NormedSpace.boundedSMul.{u1, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3) _inst_5 _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u4} γ _inst_5))) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))))) (BoundedContinuousFunction.{u2, u3} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2)) (UniformSpace.toTopologicalSpace.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2)) (PseudoMetricSpace.toUniformSpace.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2)) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u2, u3} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2)))) (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u2, u3} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2) (AddCommGroup.toAddCommMonoid.{u3} β (SeminormedAddCommGroup.toAddCommGroup.{u3} β _inst_2)) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} β _inst_2)) (BoundedContinuousFunction.{u2, u4} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ _inst_5)) (UniformSpace.toTopologicalSpace.{max u2 u4} (BoundedContinuousFunction.{u2, u4} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ _inst_5)) (PseudoMetricSpace.toUniformSpace.{max u2 u4} (BoundedContinuousFunction.{u2, u4} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ _inst_5)) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u2, u4} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ _inst_5)))) (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u2, u4} α γ _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ _inst_5) (AddCommGroup.toAddCommMonoid.{u4} γ (SeminormedAddCommGroup.toAddCommGroup.{u4} γ _inst_5)) (SeminormedAddCommGroup.to_lipschitzAdd.{u4} γ _inst_5)) (BoundedContinuousFunction.module.{u2, u3, u1} α β 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (AddCommGroup.toAddCommMonoid.{u3} β (SeminormedAddCommGroup.toAddCommGroup.{u3} β _inst_2)) (NormedSpace.toModule.{u1, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3) _inst_2 _inst_4) (NormedSpace.boundedSMul.{u1, u3} 𝕜 β 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_inst_3))))) (AddCommGroup.toAddCommMonoid.{u4} γ (SeminormedAddCommGroup.toAddCommGroup.{u4} γ _inst_5)) (NormedSpace.toModule.{u1, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3) _inst_5 _inst_6) (NormedSpace.boundedSMul.{u1, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3) _inst_5 _inst_6) (SeminormedAddCommGroup.to_lipschitzAdd.{u4} γ _inst_5))))) (ContinuousLinearMap.compLeftContinuousBounded.{u2, u3, u4, u1} α β γ 𝕜 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 g) f) x) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (ContinuousLinearMap.{u1, u1, u3, u4} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (RingHom.id.{u1} 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β) => γ) _x) (ContinuousMapClass.toFunLike.{max u3 u4, u3, u4} (ContinuousLinearMap.{u1, u1, u3, u4} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2))) (AddCommGroup.toAddCommMonoid.{u3} β (SeminormedAddCommGroup.toAddCommGroup.{u3} β _inst_2)) γ (UniformSpace.toTopologicalSpace.{u4} γ 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_inst_3))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2))) (AddCommGroup.toAddCommMonoid.{u3} β (SeminormedAddCommGroup.toAddCommGroup.{u3} β _inst_2)) γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ _inst_5))) (AddCommGroup.toAddCommMonoid.{u4} γ (SeminormedAddCommGroup.toAddCommGroup.{u4} γ _inst_5)) (NormedSpace.toModule.{u1, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u1} 𝕜 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(UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ _inst_5))) (AddCommGroup.toAddCommMonoid.{u4} γ (SeminormedAddCommGroup.toAddCommGroup.{u4} γ _inst_5)) (NormedSpace.toModule.{u1, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3) _inst_2 _inst_4) (NormedSpace.toModule.{u1, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3) _inst_5 _inst_6) (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u3, u4} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))))) β (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2))) (AddCommGroup.toAddCommMonoid.{u3} β (SeminormedAddCommGroup.toAddCommGroup.{u3} β _inst_2)) γ (UniformSpace.toTopologicalSpace.{u4} γ (PseudoMetricSpace.toUniformSpace.{u4} γ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} γ _inst_5))) (AddCommGroup.toAddCommMonoid.{u4} γ (SeminormedAddCommGroup.toAddCommGroup.{u4} γ _inst_5)) (NormedSpace.toModule.{u1, u3} 𝕜 β (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3) _inst_2 _inst_4) (NormedSpace.toModule.{u1, u4} 𝕜 γ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3) _inst_5 _inst_6)))) g (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (BoundedContinuousFunction.{u2, u3} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2)) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u2 u3, u2, u3} (BoundedContinuousFunction.{u2, u3} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2)) α β _inst_1 (UniformSpace.toTopologicalSpace.{u3} β (PseudoMetricSpace.toUniformSpace.{u3} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2))) (BoundedContinuousMapClass.toContinuousMapClass.{max u2 u3, u2, u3} (BoundedContinuousFunction.{u2, u3} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2)) α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u2, u3} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_2)))) f x))
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.comp_left_continuous_bounded_apply ContinuousLinearMap.compLeftContinuousBounded_applyₓ'. -/
 @[simp]
 theorem ContinuousLinearMap.compLeftContinuousBounded_apply (g : β →L[𝕜] γ) (f : α →ᵇ β) (x : α) :
     (g.compLeftContinuousBounded α f) x = g (f x) :=
@@ -1313,11 +2013,23 @@ instance : Mul (α →ᵇ R)
       le_trans (norm_mul_le (f x) (g x)) <|
         mul_le_mul (f.norm_coe_le_norm x) (g.norm_coe_le_norm x) (norm_nonneg _) (norm_nonneg _)
 
+/- warning: bounded_continuous_function.coe_mul -> BoundedContinuousFunction.coe_mul is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_mul BoundedContinuousFunction.coe_mulₓ'. -/
 @[simp]
 theorem coe_mul (f g : α →ᵇ R) : ⇑(f * g) = f * g :=
   rfl
 #align bounded_continuous_function.coe_mul BoundedContinuousFunction.coe_mul
 
+/- warning: bounded_continuous_function.mul_apply -> BoundedContinuousFunction.mul_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.mul_apply BoundedContinuousFunction.mul_applyₓ'. -/
 theorem mul_apply (f g : α →ᵇ R) (x : α) : (f * g) x = f x * g x :=
   rfl
 #align bounded_continuous_function.mul_apply BoundedContinuousFunction.mul_apply
@@ -1343,23 +2055,43 @@ section SemiNormed
 
 variable [SeminormedRing R]
 
+/- warning: bounded_continuous_function.coe_npow_rec -> BoundedContinuousFunction.coe_npowRec is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_npow_rec BoundedContinuousFunction.coe_npowRecₓ'. -/
 @[simp]
 theorem coe_npowRec (f : α →ᵇ R) : ∀ n, ⇑(npowRec n f) = f ^ n
   | 0 => by rw [npowRec, pow_zero, coe_one]
   | n + 1 => by rw [npowRec, pow_succ, coe_mul, coe_npow_rec]
 #align bounded_continuous_function.coe_npow_rec BoundedContinuousFunction.coe_npowRec
 
+#print BoundedContinuousFunction.hasNatPow /-
 instance hasNatPow : Pow (α →ᵇ R) ℕ
     where pow f n :=
     { toContinuousMap := f.toContinuousMap ^ n
       map_bounded' := by simpa [coe_npow_rec] using (npowRec n f).map_bounded' }
 #align bounded_continuous_function.has_nat_pow BoundedContinuousFunction.hasNatPow
+-/
 
+/- warning: bounded_continuous_function.coe_pow -> BoundedContinuousFunction.coe_pow is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_pow BoundedContinuousFunction.coe_powₓ'. -/
 @[simp]
 theorem coe_pow (n : ℕ) (f : α →ᵇ R) : ⇑(f ^ n) = f ^ n :=
   rfl
 #align bounded_continuous_function.coe_pow BoundedContinuousFunction.coe_pow
 
+/- warning: bounded_continuous_function.pow_apply -> BoundedContinuousFunction.pow_apply is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.pow_apply BoundedContinuousFunction.pow_applyₓ'. -/
 @[simp]
 theorem pow_apply (n : ℕ) (f : α →ᵇ R) (v : α) : (f ^ n) v = f v ^ n :=
   rfl
@@ -1368,23 +2100,35 @@ theorem pow_apply (n : ℕ) (f : α →ᵇ R) (v : α) : (f ^ n) v = f v ^ n :=
 instance : NatCast (α →ᵇ R) :=
   ⟨fun n => BoundedContinuousFunction.const _ n⟩
 
+/- warning: bounded_continuous_function.coe_nat_cast -> BoundedContinuousFunction.coe_natCast is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_nat_cast BoundedContinuousFunction.coe_natCastₓ'. -/
 @[simp, norm_cast]
-theorem coe_nat_cast (n : ℕ) : ((n : α →ᵇ R) : α → R) = n :=
+theorem coe_natCast (n : ℕ) : ((n : α →ᵇ R) : α → R) = n :=
   rfl
-#align bounded_continuous_function.coe_nat_cast BoundedContinuousFunction.coe_nat_cast
+#align bounded_continuous_function.coe_nat_cast BoundedContinuousFunction.coe_natCast
 
 instance : IntCast (α →ᵇ R) :=
   ⟨fun n => BoundedContinuousFunction.const _ n⟩
 
+/- warning: bounded_continuous_function.coe_int_cast -> BoundedContinuousFunction.coe_intCast is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_int_cast BoundedContinuousFunction.coe_intCastₓ'. -/
 @[simp, norm_cast]
-theorem coe_int_cast (n : ℤ) : ((n : α →ᵇ R) : α → R) = n :=
+theorem coe_intCast (n : ℤ) : ((n : α →ᵇ R) : α → R) = n :=
   rfl
-#align bounded_continuous_function.coe_int_cast BoundedContinuousFunction.coe_int_cast
+#align bounded_continuous_function.coe_int_cast BoundedContinuousFunction.coe_intCast
 
 instance : Ring (α →ᵇ R) :=
   FunLike.coe_injective.Ring _ coe_zero coe_one coe_add coe_mul coe_neg coe_sub
-    (fun _ _ => coe_nsmul _ _) (fun _ _ => coe_zsmul _ _) (fun _ _ => coe_pow _ _) coe_nat_cast
-    coe_int_cast
+    (fun _ _ => coe_nsmul _ _) (fun _ _ => coe_zsmul _ _) (fun _ _ => coe_pow _ _) coe_natCast
+    coe_intCast
 
 instance : SeminormedRing (α →ᵇ R) :=
   { BoundedContinuousFunction.nonUnitalSemiNormedRing with }
@@ -1437,22 +2181,30 @@ variable [NormedRing γ] [NormedAlgebra 𝕜 γ]
 
 variable {f g : α →ᵇ γ} {x : α} {c : 𝕜}
 
+#print BoundedContinuousFunction.C /-
 /-- `bounded_continuous_function.const` as a `ring_hom`. -/
-def c : 𝕜 →+* α →ᵇ γ where
+def C : 𝕜 →+* α →ᵇ γ where
   toFun := fun c : 𝕜 => const α ((algebraMap 𝕜 γ) c)
   map_one' := ext fun x => (algebraMap 𝕜 γ).map_one
   map_mul' c₁ c₂ := ext fun x => (algebraMap 𝕜 γ).map_mul _ _
   map_zero' := ext fun x => (algebraMap 𝕜 γ).map_zero
   map_add' c₁ c₂ := ext fun x => (algebraMap 𝕜 γ).map_add _ _
-#align bounded_continuous_function.C BoundedContinuousFunction.c
+#align bounded_continuous_function.C BoundedContinuousFunction.C
+-/
 
 instance : Algebra 𝕜 (α →ᵇ γ) :=
   { BoundedContinuousFunction.module,
     BoundedContinuousFunction.ring with
-    toRingHom := c
+    toRingHom := C
     commutes' := fun c f => ext fun x => Algebra.commutes' _ _
     smul_def' := fun c f => ext fun x => Algebra.smul_def' _ _ }
 
+/- warning: bounded_continuous_function.algebra_map_apply -> BoundedContinuousFunction.algebraMap_apply is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {γ : Type.{u2}} {𝕜 : Type.{u3}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : TopologicalSpace.{u1} α] [_inst_5 : NormedRing.{u2} γ] [_inst_6 : NormedAlgebra.{u3, u2} 𝕜 γ _inst_1 (NormedRing.toSeminormedRing.{u2} γ _inst_5)] (k : 𝕜) (a : α), Eq.{succ u2} γ (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u2} γ (NormedRing.toSeminormedRing.{u2} γ _inst_5))) (fun (_x : BoundedContinuousFunction.{u1, u2} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u2} γ (NormedRing.toSeminormedRing.{u2} γ _inst_5))) => α -> γ) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u2} γ (NormedRing.toSeminormedRing.{u2} γ _inst_5))) (coeFn.{max (succ u3) (succ (max u1 u2)), max (succ u3) (succ (max u1 u2))} (RingHom.{u3, max u1 u2} 𝕜 (BoundedContinuousFunction.{u1, u2} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u2} γ (NormedRing.toSeminormedRing.{u2} γ _inst_5))) (Semiring.toNonAssocSemiring.{u3} 𝕜 (CommSemiring.toSemiring.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (Semiring.toNonAssocSemiring.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u2} γ (NormedRing.toSeminormedRing.{u2} γ _inst_5))) (Ring.toSemiring.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u2} γ (NormedRing.toSeminormedRing.{u2} γ _inst_5))) (BoundedContinuousFunction.ring.{u1, u2} α _inst_2 γ (NormedRing.toSeminormedRing.{u2} γ _inst_5))))) (fun (_x : RingHom.{u3, max u1 u2} 𝕜 (BoundedContinuousFunction.{u1, u2} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u2} γ (NormedRing.toSeminormedRing.{u2} γ _inst_5))) (Semiring.toNonAssocSemiring.{u3} 𝕜 (CommSemiring.toSemiring.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (Semiring.toNonAssocSemiring.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u2} γ (NormedRing.toSeminormedRing.{u2} γ _inst_5))) (Ring.toSemiring.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u2} γ (NormedRing.toSeminormedRing.{u2} γ _inst_5))) (BoundedContinuousFunction.ring.{u1, u2} α _inst_2 γ (NormedRing.toSeminormedRing.{u2} γ _inst_5))))) => 𝕜 -> (BoundedContinuousFunction.{u1, u2} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u2} γ (NormedRing.toSeminormedRing.{u2} γ _inst_5)))) (RingHom.hasCoeToFun.{u3, max u1 u2} 𝕜 (BoundedContinuousFunction.{u1, u2} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u2} γ (NormedRing.toSeminormedRing.{u2} γ _inst_5))) (Semiring.toNonAssocSemiring.{u3} 𝕜 (CommSemiring.toSemiring.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (Semiring.toNonAssocSemiring.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u2} γ (NormedRing.toSeminormedRing.{u2} γ _inst_5))) (Ring.toSemiring.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u2} γ (NormedRing.toSeminormedRing.{u2} γ _inst_5))) (BoundedContinuousFunction.ring.{u1, u2} α _inst_2 γ (NormedRing.toSeminormedRing.{u2} γ _inst_5))))) (algebraMap.{u3, max u1 u2} 𝕜 (BoundedContinuousFunction.{u1, u2} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u2} γ (NormedRing.toSeminormedRing.{u2} γ _inst_5))) (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))) (Ring.toSemiring.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u2} γ (NormedRing.toSeminormedRing.{u2} γ _inst_5))) (BoundedContinuousFunction.ring.{u1, u2} α _inst_2 γ (NormedRing.toSeminormedRing.{u2} γ _inst_5))) (BoundedContinuousFunction.algebra.{u1, u2, u3} α γ 𝕜 _inst_1 _inst_2 _inst_5 _inst_6)) k) a) (SMul.smul.{u3, u2} 𝕜 γ (SMulZeroClass.toHasSmul.{u3, u2} 𝕜 γ (AddZeroClass.toHasZero.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (SeminormedAddCommGroup.toAddCommGroup.{u2} γ (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} γ (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} γ (NormedRing.toNonUnitalNormedRing.{u2} γ _inst_5)))))))) (SMulWithZero.toSmulZeroClass.{u3, u2} 𝕜 γ (MulZeroClass.toHasZero.{u3} 𝕜 (MulZeroOneClass.toMulZeroClass.{u3} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (SeminormedAddCommGroup.toAddCommGroup.{u2} γ (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} γ (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} γ (NormedRing.toNonUnitalNormedRing.{u2} γ _inst_5)))))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 γ (Semiring.toMonoidWithZero.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (AddCommGroup.toAddCommMonoid.{u2} γ (SeminormedAddCommGroup.toAddCommGroup.{u2} γ (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} γ (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} γ (NormedRing.toNonUnitalNormedRing.{u2} γ _inst_5)))))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 γ (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} γ (SeminormedAddCommGroup.toAddCommGroup.{u2} γ (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} γ (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} γ (NormedRing.toNonUnitalNormedRing.{u2} γ _inst_5))))) (NormedSpace.toModule.{u3, u2} 𝕜 γ _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} γ (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} γ (NormedRing.toNonUnitalNormedRing.{u2} γ _inst_5))) (NormedAlgebra.toNormedSpace'.{u3, u2} 𝕜 _inst_1 γ _inst_5 _inst_6)))))) k (OfNat.ofNat.{u2} γ 1 (OfNat.mk.{u2} γ 1 (One.one.{u2} γ (AddMonoidWithOne.toOne.{u2} γ (AddGroupWithOne.toAddMonoidWithOne.{u2} γ (AddCommGroupWithOne.toAddGroupWithOne.{u2} γ (Ring.toAddCommGroupWithOne.{u2} γ (NormedRing.toRing.{u2} γ _inst_5)))))))))
+but is expected to have type
+  forall {α : Type.{u2}} {γ : Type.{u3}} {𝕜 : Type.{u1}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u2} α] [_inst_5 : NormedRing.{u3} γ] [_inst_6 : NormedAlgebra.{u1, u3} 𝕜 γ _inst_1 (NormedRing.toSeminormedRing.{u3} γ _inst_5)] (k : 𝕜) (a : α), Eq.{succ u3} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => γ) a) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => γ) _x) (ContinuousMapClass.toFunLike.{max u2 u3, u2, u3} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) α γ _inst_2 (UniformSpace.toTopologicalSpace.{u3} γ (PseudoMetricSpace.toUniformSpace.{u3} γ (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5)))) (BoundedContinuousMapClass.toContinuousMapClass.{max u2 u3, u2, u3} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5)) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u1, max (succ u2) (succ u3)} (RingHom.{u1, max u3 u2} 𝕜 (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (Semiring.toNonAssocSemiring.{max u3 u2} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (Ring.toSemiring.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (BoundedContinuousFunction.ring.{u2, u3} α _inst_2 γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 𝕜) => BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, u1, max u2 u3} (RingHom.{u1, max u3 u2} 𝕜 (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (Semiring.toNonAssocSemiring.{max u3 u2} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (Ring.toSemiring.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (BoundedContinuousFunction.ring.{u2, u3} α _inst_2 γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))))) 𝕜 (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (NonUnitalNonAssocSemiring.toMul.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))))) (NonUnitalNonAssocSemiring.toMul.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (Semiring.toNonAssocSemiring.{max u3 u2} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (Ring.toSemiring.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (BoundedContinuousFunction.ring.{u2, u3} α _inst_2 γ (NormedRing.toSeminormedRing.{u3} γ _inst_5)))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u2 u3) u1, u1, max u2 u3} (RingHom.{u1, max u3 u2} 𝕜 (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (Semiring.toNonAssocSemiring.{max u3 u2} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (Ring.toSemiring.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (BoundedContinuousFunction.ring.{u2, u3} α _inst_2 γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))))) 𝕜 (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (Semiring.toNonAssocSemiring.{max u3 u2} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (Ring.toSemiring.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (BoundedContinuousFunction.ring.{u2, u3} α _inst_2 γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u3) u1, u1, max u2 u3} (RingHom.{u1, max u3 u2} 𝕜 (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (Semiring.toNonAssocSemiring.{max u3 u2} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (Ring.toSemiring.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (BoundedContinuousFunction.ring.{u2, u3} α _inst_2 γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))))) 𝕜 (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (Semiring.toNonAssocSemiring.{max u3 u2} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (Ring.toSemiring.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (BoundedContinuousFunction.ring.{u2, u3} α _inst_2 γ (NormedRing.toSeminormedRing.{u3} γ _inst_5)))) (RingHom.instRingHomClassRingHom.{u1, max u2 u3} 𝕜 (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (Semiring.toNonAssocSemiring.{max u3 u2} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (Ring.toSemiring.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (BoundedContinuousFunction.ring.{u2, u3} α _inst_2 γ (NormedRing.toSeminormedRing.{u3} γ _inst_5)))))))) (algebraMap.{u1, max u3 u2} 𝕜 (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α γ _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (BoundedContinuousFunction.ring.{u2, u3} α _inst_2 γ (NormedRing.toSeminormedRing.{u3} γ _inst_5))) (BoundedContinuousFunction.algebra.{u2, u3, u1} α γ 𝕜 _inst_1 _inst_2 _inst_5 _inst_6)) k) a) (HSMul.hSMul.{u1, u3, u3} 𝕜 γ γ (instHSMul.{u1, u3} 𝕜 γ (Algebra.toSMul.{u1, u3} 𝕜 γ (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u3} γ (NormedRing.toRing.{u3} γ _inst_5)) (NormedAlgebra.toAlgebra.{u1, u3} 𝕜 γ _inst_1 (NormedRing.toSeminormedRing.{u3} γ _inst_5) _inst_6))) k (OfNat.ofNat.{u3} γ 1 (One.toOfNat1.{u3} γ (Semiring.toOne.{u3} γ (Ring.toSemiring.{u3} γ (NormedRing.toRing.{u3} γ _inst_5))))))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.algebra_map_apply BoundedContinuousFunction.algebraMap_applyₓ'. -/
 @[simp]
 theorem algebraMap_apply (k : 𝕜) (a : α) : algebraMap 𝕜 (α →ᵇ γ) k a = k • 1 :=
   by
@@ -1471,6 +2223,7 @@ functions from `α` to `β` is naturally a module over the algebra of bounded co
 functions from `α` to `𝕜`. -/
 
 
+#print BoundedContinuousFunction.hasSmul' /-
 instance hasSmul' : SMul (α →ᵇ 𝕜) (α →ᵇ β) :=
   ⟨fun (f : α →ᵇ 𝕜) (g : α →ᵇ β) =>
     ofNormedAddCommGroup (fun x => f x • g x) (f.Continuous.smul g.Continuous) (‖f‖ * ‖g‖) fun x =>
@@ -1480,7 +2233,14 @@ instance hasSmul' : SMul (α →ᵇ 𝕜) (α →ᵇ β) :=
           mul_le_mul (f.norm_coe_le_norm _) (g.norm_coe_le_norm _) (norm_nonneg _) (norm_nonneg _)
         ⟩
 #align bounded_continuous_function.has_smul' BoundedContinuousFunction.hasSmul'
+-/
 
+/- warning: bounded_continuous_function.module' -> BoundedContinuousFunction.module' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {𝕜 : Type.{u3}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : SeminormedAddCommGroup.{u2} β] [_inst_4 : NormedSpace.{u3, u2} 𝕜 β _inst_1 _inst_3], Module.{max u1 u3, max u1 u2} (BoundedContinuousFunction.{u1, u3} α 𝕜 _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))))) (BoundedContinuousFunction.{u1, u2} α β _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_3)) (Ring.toSemiring.{max u1 u3} (BoundedContinuousFunction.{u1, u3} α 𝕜 _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))))) (BoundedContinuousFunction.ring.{u1, u3} α _inst_2 𝕜 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))))) (BoundedContinuousFunction.addAddCommMonoid.{u1, u2} α β _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_3) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_3)) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} β _inst_3))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {𝕜 : Type.{u3}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : SeminormedAddCommGroup.{u2} β] [_inst_4 : NormedSpace.{u3, u2} 𝕜 β _inst_1 _inst_3], Module.{max u3 u1, max u2 u1} (BoundedContinuousFunction.{u1, u3} α 𝕜 _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))))) (BoundedContinuousFunction.{u1, u2} α β _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (BoundedContinuousFunction.{u1, u3} α 𝕜 _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))))) (CommRing.toCommSemiring.{max u1 u3} (BoundedContinuousFunction.{u1, u3} α 𝕜 _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))))) (BoundedContinuousFunction.commRing.{u1, u3} α _inst_2 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))))) (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, u2} α β _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_3) (AddCommGroup.toAddCommMonoid.{u2} β (SeminormedAddCommGroup.toAddCommGroup.{u2} β _inst_3)) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} β _inst_3))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.module' BoundedContinuousFunction.module'ₓ'. -/
 instance module' : Module (α →ᵇ 𝕜) (α →ᵇ β) :=
   Module.ofCore <|
     { smul := (· • ·)
@@ -1490,6 +2250,12 @@ instance module' : Module (α →ᵇ 𝕜) (α →ᵇ β) :=
       one_smul := fun f => ext fun x => one_smul 𝕜 (f x) }
 #align bounded_continuous_function.module' BoundedContinuousFunction.module'
 
+/- warning: bounded_continuous_function.norm_smul_le -> BoundedContinuousFunction.norm_smul_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {𝕜 : Type.{u3}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : SeminormedAddCommGroup.{u2} β] [_inst_4 : NormedSpace.{u3, u2} 𝕜 β _inst_1 _inst_3] (f : BoundedContinuousFunction.{u1, u3} α 𝕜 _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))))) (g : BoundedContinuousFunction.{u1, u2} α β _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_3)), LE.le.{0} Real Real.hasLe (Norm.norm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_3)) (BoundedContinuousFunction.hasNorm.{u1, u2} α β _inst_2 _inst_3) (SMul.smul.{max u1 u3, max u1 u2} (BoundedContinuousFunction.{u1, u3} α 𝕜 _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))))) (BoundedContinuousFunction.{u1, u2} α β _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_3)) (BoundedContinuousFunction.hasSmul'.{u1, u2, u3} α β 𝕜 _inst_1 _inst_2 _inst_3 _inst_4) f g)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{max u1 u3} (BoundedContinuousFunction.{u1, u3} α 𝕜 _inst_2 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))))) (BoundedContinuousFunction.hasNorm.{u1, u3} α 𝕜 _inst_2 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u3} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u3} 𝕜 (NormedRing.toNonUnitalNormedRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))))) f) (Norm.norm.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_3)) (BoundedContinuousFunction.hasNorm.{u1, u2} α β _inst_2 _inst_3) g))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u3}} {𝕜 : Type.{u1}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : SeminormedAddCommGroup.{u3} β] [_inst_4 : NormedSpace.{u1, u3} 𝕜 β _inst_1 _inst_3] (f : BoundedContinuousFunction.{u2, u1} α 𝕜 _inst_2 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (g : BoundedContinuousFunction.{u2, u3} α β _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_3)), LE.le.{0} Real Real.instLEReal (Norm.norm.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α β _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_3)) (BoundedContinuousFunction.instNormBoundedContinuousFunctionToPseudoMetricSpace.{u2, u3} α β _inst_2 _inst_3) (HSMul.hSMul.{max u2 u1, max u2 u3, max u2 u3} (BoundedContinuousFunction.{u2, u1} α 𝕜 _inst_2 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (BoundedContinuousFunction.{u2, u3} α β _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_3)) (BoundedContinuousFunction.{u2, u3} α β _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_3)) (instHSMul.{max u2 u1, max u2 u3} (BoundedContinuousFunction.{u2, u1} α 𝕜 _inst_2 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (BoundedContinuousFunction.{u2, u3} α β _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_3)) (BoundedContinuousFunction.hasSmul'.{u2, u3, u1} α β 𝕜 _inst_1 _inst_2 _inst_3 _inst_4)) f g)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{max u2 u1} (BoundedContinuousFunction.{u2, u1} α 𝕜 _inst_2 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (BoundedContinuousFunction.instNormBoundedContinuousFunctionToPseudoMetricSpace.{u2, u1} α 𝕜 _inst_2 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) f) (Norm.norm.{max u2 u3} (BoundedContinuousFunction.{u2, u3} α β _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} β _inst_3)) (BoundedContinuousFunction.instNormBoundedContinuousFunctionToPseudoMetricSpace.{u2, u3} α β _inst_2 _inst_3) g))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.norm_smul_le BoundedContinuousFunction.norm_smul_leₓ'. -/
 theorem norm_smul_le (f : α →ᵇ 𝕜) (g : α →ᵇ β) : ‖f • g‖ ≤ ‖f‖ * ‖g‖ :=
   norm_ofNormedAddCommGroup_le _ (mul_nonneg (norm_nonneg _) (norm_nonneg _)) _
 #align bounded_continuous_function.norm_smul_le BoundedContinuousFunction.norm_smul_le
@@ -1499,6 +2265,12 @@ show that the space of bounded continuous functions from `α` to `β` is natural
 module over the algebra of bounded continuous functions from `α` to `𝕜`. -/
 end NormedAlgebra
 
+/- warning: bounded_continuous_function.nnreal.upper_bound -> BoundedContinuousFunction.Nnreal.upper_bound is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (f : BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) (x : α), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) => α -> NNReal) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) f x) (NNDist.nndist.{u1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) (PseudoMetricSpace.toNNDist.{u1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) (BoundedContinuousFunction.pseudoMetricSpace.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace)) f (OfNat.ofNat.{u1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) 0 (OfNat.mk.{u1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) 0 (Zero.zero.{u1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) (BoundedContinuousFunction.hasZero.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (f : BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) (x : α), LE.le.{0} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => NNReal) x) (Preorder.toLE.{0} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => NNReal) x) (PartialOrder.toPreorder.{0} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => NNReal) x) (StrictOrderedSemiring.toPartialOrder.{0} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => NNReal) x) instNNRealStrictOrderedSemiring))) (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => NNReal) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) α NNReal _inst_1 (UniformSpace.toTopologicalSpace.{0} NNReal (PseudoMetricSpace.toUniformSpace.{0} NNReal instPseudoMetricSpaceNNReal)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) α NNReal _inst_1 instPseudoMetricSpaceNNReal (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal))) f x) (NNDist.nndist.{u1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) (PseudoMetricSpace.toNNDist.{u1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) (BoundedContinuousFunction.instPseudoMetricSpaceBoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal)) f (OfNat.ofNat.{u1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) 0 (Zero.toOfNat0.{u1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) (BoundedContinuousFunction.instZeroBoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealZero))))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.nnreal.upper_bound BoundedContinuousFunction.Nnreal.upper_boundₓ'. -/
 theorem Nnreal.upper_bound {α : Type _} [TopologicalSpace α] (f : α →ᵇ ℝ≥0) (x : α) :
     f x ≤ nndist f 0 :=
   by
@@ -1538,6 +2310,12 @@ instance : StarAddMonoid (α →ᵇ β)
   star_involutive f := ext fun x => star_star (f x)
   star_add f g := ext fun x => star_add (f x) (g x)
 
+/- warning: bounded_continuous_function.coe_star -> BoundedContinuousFunction.coe_star is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_3 : TopologicalSpace.{u1} α] [_inst_4 : SeminormedAddCommGroup.{u2} β] [_inst_5 : StarAddMonoid.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_4))))] [_inst_6 : NormedStarGroup.{u2} β _inst_4 _inst_5] (f : BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)), Eq.{succ (max u1 u2)} (α -> β) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) (Star.star.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) (InvolutiveStar.toHasStar.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) (StarAddMonoid.toHasInvolutiveStar.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) (BoundedContinuousFunction.addMonoid.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4) (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} β _inst_4)) (BoundedContinuousFunction.starAddMonoid.{u1, u2} α β _inst_3 _inst_4 _inst_5 _inst_6))) f)) (Star.star.{max u1 u2} (α -> β) (Pi.hasStar.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => InvolutiveStar.toHasStar.{u2} β (StarAddMonoid.toHasInvolutiveStar.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_4)))) _inst_5))) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) f))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_3 : TopologicalSpace.{u1} α] [_inst_4 : SeminormedAddCommGroup.{u2} β] [_inst_5 : StarAddMonoid.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_4))))] [_inst_6 : NormedStarGroup.{u2} β _inst_4 _inst_5] (f : BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)), Eq.{max (succ u1) (succ u2)} (forall (ᾰ : α), (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) ᾰ) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) α β _inst_3 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4))) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)))) (Star.star.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) (InvolutiveStar.toStar.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) (StarAddMonoid.toInvolutiveStar.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) (BoundedContinuousFunction.addMonoid.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4) (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} β _inst_4)) (BoundedContinuousFunction.starAddMonoid.{u1, u2} α β _inst_3 _inst_4 _inst_5 _inst_6))) f)) (Star.star.{max u1 u2} (forall (ᾰ : α), (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) ᾰ) (Pi.instStarForAll.{u1, u2} α (fun (ᾰ : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) ᾰ) (fun (i : α) => InvolutiveStar.toStar.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) i) (StarAddMonoid.toInvolutiveStar.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) i) (SubNegMonoid.toAddMonoid.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) i) (AddGroup.toSubNegMonoid.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) i) (SeminormedAddGroup.toAddGroup.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) i) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) i) _inst_4)))) _inst_5))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) α β _inst_3 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4))) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)))) f))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_star BoundedContinuousFunction.coe_starₓ'. -/
 /-- The right-hand side of this equality can be parsed `star ∘ ⇑f` because of the
 instance `pi.has_star`. Upon inspecting the goal, one sees `⊢ ⇑(star f) = star ⇑f`.-/
 @[simp]
@@ -1545,6 +2323,12 @@ theorem coe_star (f : α →ᵇ β) : ⇑(star f) = star f :=
   rfl
 #align bounded_continuous_function.coe_star BoundedContinuousFunction.coe_star
 
+/- warning: bounded_continuous_function.star_apply -> BoundedContinuousFunction.star_apply is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_3 : TopologicalSpace.{u1} α] [_inst_4 : SeminormedAddCommGroup.{u2} β] [_inst_5 : StarAddMonoid.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_4))))] [_inst_6 : NormedStarGroup.{u2} β _inst_4 _inst_5] (f : BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) (x : α), Eq.{succ u2} β (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) (Star.star.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) (InvolutiveStar.toHasStar.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) (StarAddMonoid.toHasInvolutiveStar.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) (BoundedContinuousFunction.addMonoid.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4) (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} β _inst_4)) (BoundedContinuousFunction.starAddMonoid.{u1, u2} α β _inst_3 _inst_4 _inst_5 _inst_6))) f) x) (Star.star.{u2} β (InvolutiveStar.toHasStar.{u2} β (StarAddMonoid.toHasInvolutiveStar.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_4)))) _inst_5)) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) f x))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_3 : TopologicalSpace.{u1} α] [_inst_4 : SeminormedAddCommGroup.{u2} β] [_inst_5 : StarAddMonoid.{u2} β (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_4))))] [_inst_6 : NormedStarGroup.{u2} β _inst_4 _inst_5] (f : BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) (x : α), Eq.{succ u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) α β _inst_3 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4))) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)))) (Star.star.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) (InvolutiveStar.toStar.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) (StarAddMonoid.toInvolutiveStar.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) (BoundedContinuousFunction.addMonoid.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4) (SubNegMonoid.toAddMonoid.{u2} β (AddGroup.toSubNegMonoid.{u2} β (SeminormedAddGroup.toAddGroup.{u2} β (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} β _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} β _inst_4)) (BoundedContinuousFunction.starAddMonoid.{u1, u2} α β _inst_3 _inst_4 _inst_5 _inst_6))) f) x) (Star.star.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (InvolutiveStar.toStar.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (StarAddMonoid.toInvolutiveStar.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (SubNegMonoid.toAddMonoid.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (AddGroup.toSubNegMonoid.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (SeminormedAddGroup.toAddGroup.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) x) _inst_4)))) _inst_5)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) α β _inst_3 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4))) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)) α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_3 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β _inst_4)))) f x))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.star_apply BoundedContinuousFunction.star_applyₓ'. -/
 @[simp]
 theorem star_apply (f : α →ᵇ β) (x : α) : star f x = star (f x) :=
   rfl
@@ -1635,11 +2419,23 @@ instance : SemilatticeSup (α →ᵇ β) :=
 instance : Lattice (α →ᵇ β) :=
   { BoundedContinuousFunction.semilatticeSup, BoundedContinuousFunction.semilatticeInf with }
 
+/- warning: bounded_continuous_function.coe_fn_sup -> BoundedContinuousFunction.coeFn_sup is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : NormedLatticeAddCommGroup.{u2} β] (f : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2)))) (g : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2)))), Eq.{succ (max u1 u2)} (α -> β) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2)))) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2)))) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2)))) (Sup.sup.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2)))) (SemilatticeSup.toHasSup.{max u1 u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2)))) (BoundedContinuousFunction.semilatticeSup.{u1, u2} α β _inst_1 _inst_2)) f g)) (Sup.sup.{max u1 u2} (α -> β) (Pi.hasSup.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (NormedLatticeAddCommGroup.toLattice.{u2} β _inst_2)))) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2)))) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2)))) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2)))) f) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2)))) (fun (_x : BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2)))) => α -> β) (BoundedContinuousFunction.hasCoeToFun.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2)))) g))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_fn_sup BoundedContinuousFunction.coeFn_supₓ'. -/
 @[simp]
 theorem coeFn_sup (f g : α →ᵇ β) : ⇑(f ⊔ g) = f ⊔ g :=
   rfl
 #align bounded_continuous_function.coe_fn_sup BoundedContinuousFunction.coeFn_sup
 
+/- warning: bounded_continuous_function.coe_fn_abs -> BoundedContinuousFunction.coeFn_abs is a dubious translation:
+lean 3 declaration is
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(SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2)))) (BoundedContinuousFunction.semilatticeSup.{u1, u2} α β _inst_1 _inst_2))) f)) (Abs.abs.{max u1 u2} (forall (ᾰ : α), (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) ᾰ) (Neg.toHasAbs.{max u1 u2} (forall (ᾰ : α), (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) ᾰ) (Pi.instNeg.{u1, u2} α (fun (ᾰ : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) ᾰ) (fun (i : α) => NegZeroClass.toNeg.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) i) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) i) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) i) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) i) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) i) (NormedAddCommGroup.toAddCommGroup.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) i) (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) i) _inst_2)))))))) (Pi.instSupForAll.{u1, u2} α (fun (ᾰ : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) ᾰ) (fun (i : α) => SemilatticeSup.toSup.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) i) (Lattice.toSemilatticeSup.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) i) (NormedLatticeAddCommGroup.toLattice.{u2} ((fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) i) _inst_2))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2)))) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => β) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2)))) α β _inst_1 (UniformSpace.toTopologicalSpace.{u2} β (PseudoMetricSpace.toUniformSpace.{u2} β (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2))))) (BoundedContinuousMapClass.toContinuousMapClass.{max u1 u2, u1, u2} (BoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2)))) α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2))) (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, u2} α β _inst_1 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} β (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} β (NormedLatticeAddCommGroup.toNormedAddCommGroup.{u2} β _inst_2)))))) f))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.coe_fn_abs BoundedContinuousFunction.coeFn_absₓ'. -/
 @[simp]
 theorem coeFn_abs (f : α →ᵇ β) : ⇑(|f|) = |f| :=
   rfl
@@ -1665,17 +2461,35 @@ section NonnegativePart
 
 variable [TopologicalSpace α]
 
+/- warning: bounded_continuous_function.nnreal_part -> BoundedContinuousFunction.nnrealPart is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α], (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) -> (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α], (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) -> (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.nnreal_part BoundedContinuousFunction.nnrealPartₓ'. -/
 /-- The nonnegative part of a bounded continuous `ℝ`-valued function as a bounded
 continuous `ℝ≥0`-valued function. -/
 def nnrealPart (f : α →ᵇ ℝ) : α →ᵇ ℝ≥0 :=
   BoundedContinuousFunction.comp _ (show LipschitzWith 1 Real.toNNReal from lipschitzWith_pos) f
 #align bounded_continuous_function.nnreal_part BoundedContinuousFunction.nnrealPart
 
+/- warning: bounded_continuous_function.nnreal_part_coe_fun_eq -> BoundedContinuousFunction.nnrealPart_coeFn_eq is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (f : BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace), Eq.{succ u1} (α -> NNReal) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) => α -> NNReal) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) (BoundedContinuousFunction.nnrealPart.{u1} α _inst_1 f)) (Function.comp.{succ u1, 1, 1} α Real NNReal Real.toNNReal (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) => α -> Real) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) f))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (f : BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace), Eq.{succ u1} (forall (ᾰ : α), (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => NNReal) ᾰ) (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => NNReal) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) α NNReal _inst_1 (UniformSpace.toTopologicalSpace.{0} NNReal (PseudoMetricSpace.toUniformSpace.{0} NNReal instPseudoMetricSpaceNNReal)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) α NNReal _inst_1 instPseudoMetricSpaceNNReal (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal))) (BoundedContinuousFunction.nnrealPart.{u1} α _inst_1 f)) (Function.comp.{succ u1, 1, 1} α Real NNReal Real.toNNReal (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) α Real _inst_1 Real.pseudoMetricSpace (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace))) f))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.nnreal_part_coe_fun_eq BoundedContinuousFunction.nnrealPart_coeFn_eqₓ'. -/
 @[simp]
-theorem nnrealPart_coe_fun_eq (f : α →ᵇ ℝ) : ⇑f.nnrealPart = Real.toNNReal ∘ ⇑f :=
+theorem nnrealPart_coeFn_eq (f : α →ᵇ ℝ) : ⇑f.nnrealPart = Real.toNNReal ∘ ⇑f :=
   rfl
-#align bounded_continuous_function.nnreal_part_coe_fun_eq BoundedContinuousFunction.nnrealPart_coe_fun_eq
-
+#align bounded_continuous_function.nnreal_part_coe_fun_eq BoundedContinuousFunction.nnrealPart_coeFn_eq
+
+/- warning: bounded_continuous_function.nnnorm -> BoundedContinuousFunction.nnnorm is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α], (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) -> (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α], (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) -> (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal)
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.nnnorm BoundedContinuousFunction.nnnormₓ'. -/
 /-- The absolute value of a bounded continuous `ℝ`-valued function as a bounded
 continuous `ℝ≥0`-valued function. -/
 def nnnorm (f : α →ᵇ ℝ) : α →ᵇ ℝ≥0 :=
@@ -1683,11 +2497,23 @@ def nnnorm (f : α →ᵇ ℝ) : α →ᵇ ℝ≥0 :=
     (show LipschitzWith 1 fun x : ℝ => ‖x‖₊ from lipschitzWith_one_norm) f
 #align bounded_continuous_function.nnnorm BoundedContinuousFunction.nnnorm
 
+/- warning: bounded_continuous_function.nnnorm_coe_fun_eq -> BoundedContinuousFunction.nnnorm_coeFn_eq is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (f : BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace), Eq.{succ u1} (α -> NNReal) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) => α -> NNReal) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) (BoundedContinuousFunction.nnnorm.{u1} α _inst_1 f)) (Function.comp.{succ u1, 1, 1} α Real NNReal (NNNorm.nnnorm.{0} Real (SeminormedAddGroup.toNNNorm.{0} Real (SeminormedAddCommGroup.toSeminormedAddGroup.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing))))))) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) => α -> Real) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) f))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (f : BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace), Eq.{succ u1} (forall (ᾰ : α), (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => NNReal) ᾰ) (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => NNReal) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) α NNReal _inst_1 (UniformSpace.toTopologicalSpace.{0} NNReal (PseudoMetricSpace.toUniformSpace.{0} NNReal instPseudoMetricSpaceNNReal)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) α NNReal _inst_1 instPseudoMetricSpaceNNReal (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal))) (BoundedContinuousFunction.nnnorm.{u1} α _inst_1 f)) (Function.comp.{succ u1, 1, 1} α Real NNReal (NNNorm.nnnorm.{0} Real (SeminormedAddGroup.toNNNorm.{0} Real (SeminormedAddCommGroup.toSeminormedAddGroup.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing))))))) (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) α Real _inst_1 Real.pseudoMetricSpace (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace))) f))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.nnnorm_coe_fun_eq BoundedContinuousFunction.nnnorm_coeFn_eqₓ'. -/
 @[simp]
-theorem nnnorm_coe_fun_eq (f : α →ᵇ ℝ) : ⇑f.nnnorm = NNNorm.nnnorm ∘ ⇑f :=
+theorem nnnorm_coeFn_eq (f : α →ᵇ ℝ) : ⇑f.nnnorm = NNNorm.nnnorm ∘ ⇑f :=
   rfl
-#align bounded_continuous_function.nnnorm_coe_fun_eq BoundedContinuousFunction.nnnorm_coe_fun_eq
-
+#align bounded_continuous_function.nnnorm_coe_fun_eq BoundedContinuousFunction.nnnorm_coeFn_eq
+
+/- warning: bounded_continuous_function.self_eq_nnreal_part_sub_nnreal_part_neg -> BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_neg is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (f : BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace), Eq.{succ u1} (α -> Real) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) => α -> Real) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) f) (HSub.hSub.{u1, u1, u1} (α -> Real) (α -> Real) (α -> Real) (instHSub.{u1} (α -> Real) (Pi.instSub.{u1, 0} α (fun (ᾰ : α) => Real) (fun (i : α) => Real.hasSub))) (Function.comp.{succ u1, 1, 1} α NNReal Real ((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)))) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) => α -> NNReal) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) (BoundedContinuousFunction.nnrealPart.{u1} α _inst_1 f))) (Function.comp.{succ u1, 1, 1} α NNReal Real ((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)))) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) => α -> NNReal) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) (BoundedContinuousFunction.nnrealPart.{u1} α _inst_1 (Neg.neg.{u1} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) (BoundedContinuousFunction.hasNeg.{u1, 0} α Real _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing))))) f)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (f : BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace), Eq.{succ u1} (forall (ᾰ : α), (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => Real) ᾰ) (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) α Real _inst_1 Real.pseudoMetricSpace (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace))) f) (HSub.hSub.{u1, u1, u1} (α -> Real) (α -> Real) (forall (ᾰ : α), (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => Real) ᾰ) (instHSub.{u1} (α -> Real) (Pi.instSub.{u1, 0} α (fun (ᾰ : α) => Real) (fun (i : α) => Real.instSubReal))) (Function.comp.{succ u1, 1, 1} α NNReal Real NNReal.toReal (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => NNReal) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) α NNReal _inst_1 (UniformSpace.toTopologicalSpace.{0} NNReal (PseudoMetricSpace.toUniformSpace.{0} NNReal instPseudoMetricSpaceNNReal)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) α NNReal _inst_1 instPseudoMetricSpaceNNReal (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal))) (BoundedContinuousFunction.nnrealPart.{u1} α _inst_1 f))) (Function.comp.{succ u1, 1, 1} α NNReal Real NNReal.toReal (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => NNReal) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) α NNReal _inst_1 (UniformSpace.toTopologicalSpace.{0} NNReal (PseudoMetricSpace.toUniformSpace.{0} NNReal instPseudoMetricSpaceNNReal)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) α NNReal _inst_1 instPseudoMetricSpaceNNReal (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal))) (BoundedContinuousFunction.nnrealPart.{u1} α _inst_1 (Neg.neg.{u1} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) (BoundedContinuousFunction.instNegBoundedContinuousFunctionToPseudoMetricSpace.{u1, 0} α Real _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing))))) f)))))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.self_eq_nnreal_part_sub_nnreal_part_neg BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_negₓ'. -/
 /-- Decompose a bounded continuous function to its positive and negative parts. -/
 theorem self_eq_nnrealPart_sub_nnrealPart_neg (f : α →ᵇ ℝ) :
     ⇑f = coe ∘ f.nnrealPart - coe ∘ (-f).nnrealPart :=
@@ -1697,6 +2523,12 @@ theorem self_eq_nnrealPart_sub_nnrealPart_neg (f : α →ᵇ ℝ) :
   simp only [max_zero_sub_max_neg_zero_eq_self]
 #align bounded_continuous_function.self_eq_nnreal_part_sub_nnreal_part_neg BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_neg
 
+/- warning: bounded_continuous_function.abs_self_eq_nnreal_part_add_nnreal_part_neg -> BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_neg is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (f : BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace), Eq.{succ u1} (α -> Real) (Function.comp.{succ u1, 1, 1} α Real Real (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) => α -> Real) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) f)) (HAdd.hAdd.{u1, u1, u1} (α -> Real) (α -> Real) (α -> Real) (instHAdd.{u1} (α -> Real) (Pi.instAdd.{u1, 0} α (fun (ᾰ : α) => Real) (fun (i : α) => Real.hasAdd))) (Function.comp.{succ u1, 1, 1} α NNReal Real ((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)))) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) => α -> NNReal) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) (BoundedContinuousFunction.nnrealPart.{u1} α _inst_1 f))) (Function.comp.{succ u1, 1, 1} α NNReal Real ((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)))) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) => α -> NNReal) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} α NNReal _inst_1 NNReal.pseudoMetricSpace) (BoundedContinuousFunction.nnrealPart.{u1} α _inst_1 (Neg.neg.{u1} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) (BoundedContinuousFunction.hasNeg.{u1, 0} α Real _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing))))) f)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (f : BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace), Eq.{succ u1} (α -> Real) (Function.comp.{succ u1, 1, 1} α Real Real (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) α Real _inst_1 Real.pseudoMetricSpace (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace))) f)) (HAdd.hAdd.{u1, u1, u1} (α -> Real) (α -> Real) (α -> Real) (instHAdd.{u1} (α -> Real) (Pi.instAdd.{u1, 0} α (fun (ᾰ : α) => Real) (fun (i : α) => Real.instAddReal))) (Function.comp.{succ u1, 1, 1} α NNReal Real NNReal.toReal (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => NNReal) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) α NNReal _inst_1 (UniformSpace.toTopologicalSpace.{0} NNReal (PseudoMetricSpace.toUniformSpace.{0} NNReal instPseudoMetricSpaceNNReal)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) α NNReal _inst_1 instPseudoMetricSpaceNNReal (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal))) (BoundedContinuousFunction.nnrealPart.{u1} α _inst_1 f))) (Function.comp.{succ u1, 1, 1} α NNReal Real NNReal.toReal (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) α (fun (_x : α) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : α) => NNReal) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) α NNReal _inst_1 (UniformSpace.toTopologicalSpace.{0} NNReal (PseudoMetricSpace.toUniformSpace.{0} NNReal instPseudoMetricSpaceNNReal)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal) α NNReal _inst_1 instPseudoMetricSpaceNNReal (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} α NNReal _inst_1 instPseudoMetricSpaceNNReal))) (BoundedContinuousFunction.nnrealPart.{u1} α _inst_1 (Neg.neg.{u1} (BoundedContinuousFunction.{u1, 0} α Real _inst_1 Real.pseudoMetricSpace) (BoundedContinuousFunction.instNegBoundedContinuousFunctionToPseudoMetricSpace.{u1, 0} α Real _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing))))) f)))))
+Case conversion may be inaccurate. Consider using '#align bounded_continuous_function.abs_self_eq_nnreal_part_add_nnreal_part_neg BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_negₓ'. -/
 /-- Express the absolute value of a bounded continuous function in terms of its
 positive and negative parts. -/
 theorem abs_self_eq_nnrealPart_add_nnrealPart_neg (f : α →ᵇ ℝ) :

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

@@ -160,9 +160,9 @@ def mkOfDiscrete [DiscreteTopology α] (f : α → β) (C : ℝ) (h : ∀ x y :
 
 /-- The uniform distance between two bounded continuous functions -/
 instance : Dist (α →ᵇ β) :=
-  ⟨fun f g => infₛ { C | 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C }⟩
+  ⟨fun f g => sInf { C | 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C }⟩
 
-theorem dist_eq : dist f g = infₛ { C | 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C } :=
+theorem dist_eq : dist f g = sInf { C | 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C } :=
   rfl
 #align bounded_continuous_function.dist_eq BoundedContinuousFunction.dist_eq
 
@@ -176,19 +176,19 @@ theorem dist_set_exists : ∃ C, 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C
 
 /-- The pointwise distance is controlled by the distance between functions, by definition. -/
 theorem dist_coe_le_dist (x : α) : dist (f x) (g x) ≤ dist f g :=
-  le_cinfₛ dist_set_exists fun b hb => hb.2 x
+  le_csInf dist_set_exists fun b hb => hb.2 x
 #align bounded_continuous_function.dist_coe_le_dist BoundedContinuousFunction.dist_coe_le_dist
 
 /- This lemma will be needed in the proof of the metric space instance, but it will become
 useless afterwards as it will be superseded by the general result that the distance is nonnegative
 in metric spaces. -/
 private theorem dist_nonneg' : 0 ≤ dist f g :=
-  le_cinfₛ dist_set_exists fun C => And.left
+  le_csInf dist_set_exists fun C => And.left
 #align bounded_continuous_function.dist_nonneg' bounded_continuous_function.dist_nonneg'
 
 /-- The distance between two functions is controlled by the supremum of the pointwise distances -/
 theorem dist_le (C0 : (0 : ℝ) ≤ C) : dist f g ≤ C ↔ ∀ x : α, dist (f x) (g x) ≤ C :=
-  ⟨fun h x => le_trans (dist_coe_le_dist x) h, fun H => cinfₛ_le ⟨0, fun C => And.left⟩ ⟨C0, H⟩⟩
+  ⟨fun h x => le_trans (dist_coe_le_dist x) h, fun H => csInf_le ⟨0, fun C => And.left⟩ ⟨C0, H⟩⟩
 #align bounded_continuous_function.dist_le BoundedContinuousFunction.dist_le
 
 theorem dist_le_iff_of_nonempty [Nonempty α] : dist f g ≤ C ↔ ∀ x, dist (f x) (g x) ≤ C :=
@@ -218,7 +218,7 @@ theorem dist_lt_iff_of_compact [CompactSpace α] (C0 : (0 : ℝ) < C) :
       convert C0
       apply le_antisymm _ dist_nonneg'
       rw [dist_eq]
-      exact cinfₛ_le ⟨0, fun C => And.left⟩ ⟨le_rfl, fun x => False.elim (h (Nonempty.intro x))⟩
+      exact csInf_le ⟨0, fun C => And.left⟩ ⟨le_rfl, fun x => False.elim (h (Nonempty.intro x))⟩
 #align bounded_continuous_function.dist_lt_iff_of_compact BoundedContinuousFunction.dist_lt_iff_of_compact
 
 theorem dist_lt_iff_of_nonempty_compact [Nonempty α] [CompactSpace α] :
@@ -240,10 +240,10 @@ instance {α β} [TopologicalSpace α] [MetricSpace β] : MetricSpace (α →ᵇ
     where eq_of_dist_eq_zero f g hfg := by
     ext x <;> exact eq_of_dist_eq_zero (le_antisymm (hfg ▸ dist_coe_le_dist _) dist_nonneg)
 
-theorem nndist_eq : nndist f g = infₛ { C | ∀ x : α, nndist (f x) (g x) ≤ C } :=
+theorem nndist_eq : nndist f g = sInf { C | ∀ x : α, nndist (f x) (g x) ≤ C } :=
   Subtype.ext <|
     dist_eq.trans <| by
-      rw [NNReal.coe_infₛ, NNReal.coe_image]
+      rw [NNReal.coe_sInf, NNReal.coe_image]
       simp_rw [mem_set_of_eq, ← NNReal.coe_le_coe, Subtype.coe_mk, exists_prop, coe_nndist]
 #align bounded_continuous_function.nndist_eq BoundedContinuousFunction.nndist_eq
 
@@ -260,16 +260,16 @@ theorem dist_zero_of_empty [IsEmpty α] : dist f g = 0 := by
   rw [(ext isEmptyElim : f = g), dist_self]
 #align bounded_continuous_function.dist_zero_of_empty BoundedContinuousFunction.dist_zero_of_empty
 
-theorem dist_eq_supᵢ : dist f g = ⨆ x : α, dist (f x) (g x) :=
+theorem dist_eq_iSup : dist f g = ⨆ x : α, dist (f x) (g x) :=
   by
-  cases isEmpty_or_nonempty α; · rw [supᵢ_of_empty', Real.supₛ_empty, dist_zero_of_empty]
-  refine' (dist_le_iff_of_nonempty.mpr <| le_csupᵢ _).antisymm (csupᵢ_le dist_coe_le_dist)
+  cases isEmpty_or_nonempty α; · rw [iSup_of_empty', Real.sSup_empty, dist_zero_of_empty]
+  refine' (dist_le_iff_of_nonempty.mpr <| le_ciSup _).antisymm (ciSup_le dist_coe_le_dist)
   exact dist_set_exists.imp fun C hC => forall_range_iff.2 hC.2
-#align bounded_continuous_function.dist_eq_supr BoundedContinuousFunction.dist_eq_supᵢ
+#align bounded_continuous_function.dist_eq_supr BoundedContinuousFunction.dist_eq_iSup
 
-theorem nndist_eq_supᵢ : nndist f g = ⨆ x : α, nndist (f x) (g x) :=
-  Subtype.ext <| dist_eq_supᵢ.trans <| by simp_rw [NNReal.coe_supᵢ, coe_nndist]
-#align bounded_continuous_function.nndist_eq_supr BoundedContinuousFunction.nndist_eq_supᵢ
+theorem nndist_eq_iSup : nndist f g = ⨆ x : α, nndist (f x) (g x) :=
+  Subtype.ext <| dist_eq_iSup.trans <| by simp_rw [NNReal.coe_iSup, coe_nndist]
+#align bounded_continuous_function.nndist_eq_supr BoundedContinuousFunction.nndist_eq_iSup
 
 theorem tendsto_iff_tendstoUniformly {ι : Type _} {F : ι → α →ᵇ β} {f : α →ᵇ β} {l : Filter ι} :
     Tendsto F l (𝓝 f) ↔ TendstoUniformly (fun i => F i) f l :=
@@ -847,13 +847,13 @@ theorem norm_def : ‖f‖ = dist f 0 :=
 
 /-- The norm of a bounded continuous function is the supremum of `‖f x‖`.
 We use `Inf` to ensure that the definition works if `α` has no elements. -/
-theorem norm_eq (f : α →ᵇ β) : ‖f‖ = infₛ { C : ℝ | 0 ≤ C ∧ ∀ x : α, ‖f x‖ ≤ C } := by
+theorem norm_eq (f : α →ᵇ β) : ‖f‖ = sInf { C : ℝ | 0 ≤ C ∧ ∀ x : α, ‖f x‖ ≤ C } := by
   simp [norm_def, BoundedContinuousFunction.dist_eq]
 #align bounded_continuous_function.norm_eq BoundedContinuousFunction.norm_eq
 
 /-- When the domain is non-empty, we do not need the `0 ≤ C` condition in the formula for ‖f‖ as an
 `Inf`. -/
-theorem norm_eq_of_nonempty [h : Nonempty α] : ‖f‖ = infₛ { C : ℝ | ∀ x : α, ‖f x‖ ≤ C } :=
+theorem norm_eq_of_nonempty [h : Nonempty α] : ‖f‖ = sInf { C : ℝ | ∀ x : α, ‖f x‖ ≤ C } :=
   by
   obtain ⟨a⟩ := h
   rw [norm_eq]
@@ -981,13 +981,13 @@ theorem bddAbove_range_norm_comp : BddAbove <| Set.range <| norm ∘ f :=
   (Real.bounded_iff_bddBelow_bddAbove.mp <| @bounded_range _ _ _ _ f.normComp).2
 #align bounded_continuous_function.bdd_above_range_norm_comp BoundedContinuousFunction.bddAbove_range_norm_comp
 
-theorem norm_eq_supᵢ_norm : ‖f‖ = ⨆ x : α, ‖f x‖ := by
+theorem norm_eq_iSup_norm : ‖f‖ = ⨆ x : α, ‖f x‖ := by
   simp_rw [norm_def, dist_eq_supr, coe_zero, Pi.zero_apply, dist_zero_right]
-#align bounded_continuous_function.norm_eq_supr_norm BoundedContinuousFunction.norm_eq_supᵢ_norm
+#align bounded_continuous_function.norm_eq_supr_norm BoundedContinuousFunction.norm_eq_iSup_norm
 
 /-- If `‖(1 : β)‖ = 1`, then `‖(1 : α →ᵇ β)‖ = 1` if `α` is nonempty. -/
 instance [Nonempty α] [One β] [NormOneClass β] : NormOneClass (α →ᵇ β)
-    where norm_one := by simp only [norm_eq_supr_norm, coe_one, Pi.one_apply, norm_one, csupᵢ_const]
+    where norm_one := by simp only [norm_eq_supr_norm, coe_one, Pi.one_apply, norm_one, ciSup_const]
 
 /-- The pointwise opposite of a bounded continuous function is again bounded continuous. -/
 instance : Neg (α →ᵇ β) :=
@@ -1093,9 +1093,9 @@ theorem nnnorm_const_eq [h : Nonempty α] (b : β) : ‖const α b‖₊ = ‖b
   Subtype.ext <| norm_const_eq _
 #align bounded_continuous_function.nnnorm_const_eq BoundedContinuousFunction.nnnorm_const_eq
 
-theorem nnnorm_eq_supᵢ_nnnorm : ‖f‖₊ = ⨆ x : α, ‖f x‖₊ :=
-  Subtype.ext <| (norm_eq_supᵢ_norm f).trans <| by simp_rw [NNReal.coe_supᵢ, coe_nnnorm]
-#align bounded_continuous_function.nnnorm_eq_supr_nnnorm BoundedContinuousFunction.nnnorm_eq_supᵢ_nnnorm
+theorem nnnorm_eq_iSup_nnnorm : ‖f‖₊ = ⨆ x : α, ‖f x‖₊ :=
+  Subtype.ext <| (norm_eq_iSup_norm f).trans <| by simp_rw [NNReal.coe_iSup, coe_nnnorm]
+#align bounded_continuous_function.nnnorm_eq_supr_nnnorm BoundedContinuousFunction.nnnorm_eq_iSup_nnnorm
 
 theorem abs_diff_coe_le_dist : ‖f x - g x‖ ≤ dist f g :=
   by

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Mario Carneiro, Yury Kudryashov, Heather Macbeth
 
 ! This file was ported from Lean 3 source module topology.continuous_function.bounded
-! leanprover-community/mathlib commit d3af0609f6db8691dffdc3e1fb7feb7da72698f2
+! leanprover-community/mathlib commit 5dc275ec639221ca4d5f56938eb966f6ad9bc89f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1655,7 +1655,7 @@ instance : NormedLatticeAddCommGroup (α →ᵇ β) :=
       exact h₁ _
     solid := by
       intro f g h
-      have i1 : ∀ t, ‖f t‖ ≤ ‖g t‖ := fun t => solid (h t)
+      have i1 : ∀ t, ‖f t‖ ≤ ‖g t‖ := fun t => HasSolidNorm.solid (h t)
       rw [norm_le (norm_nonneg _)]
       exact fun t => (i1 t).trans (norm_coe_le_norm g t) }
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/28b2a92f2996d28e580450863c130955de0ed398

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Mario Carneiro, Yury Kudryashov, Heather Macbeth
 
 ! This file was ported from Lean 3 source module topology.continuous_function.bounded
-! leanprover-community/mathlib commit 5dc275ec639221ca4d5f56938eb966f6ad9bc89f
+! leanprover-community/mathlib commit d3af0609f6db8691dffdc3e1fb7feb7da72698f2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1655,7 +1655,7 @@ instance : NormedLatticeAddCommGroup (α →ᵇ β) :=
       exact h₁ _
     solid := by
       intro f g h
-      have i1 : ∀ t, ‖f t‖ ≤ ‖g t‖ := fun t => HasSolidNorm.solid (h t)
+      have i1 : ∀ t, ‖f t‖ ≤ ‖g t‖ := fun t => solid (h t)
       rw [norm_le (norm_nonneg _)]
       exact fun t => (i1 t).trans (norm_coe_le_norm g t) }
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Mario Carneiro, Yury Kudryashov, Heather Macbeth
 
 ! This file was ported from Lean 3 source module topology.continuous_function.bounded
-! leanprover-community/mathlib commit d3af0609f6db8691dffdc3e1fb7feb7da72698f2
+! leanprover-community/mathlib commit 5dc275ec639221ca4d5f56938eb966f6ad9bc89f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1655,7 +1655,7 @@ instance : NormedLatticeAddCommGroup (α →ᵇ β) :=
       exact h₁ _
     solid := by
       intro f g h
-      have i1 : ∀ t, ‖f t‖ ≤ ‖g t‖ := fun t => solid (h t)
+      have i1 : ∀ t, ‖f t‖ ≤ ‖g t‖ := fun t => HasSolidNorm.solid (h t)
       rw [norm_le (norm_nonneg _)]
       exact fun t => (i1 t).trans (norm_coe_le_norm g t) }
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/55d771df074d0dd020139ee1cd4b95521422df9f

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Mario Carneiro, Yury Kudryashov, Heather Macbeth
 
 ! This file was ported from Lean 3 source module topology.continuous_function.bounded
-! leanprover-community/mathlib commit 6efec6bb9fcaed3cf1baaddb2eaadd8a2a06679c
+! leanprover-community/mathlib commit d3af0609f6db8691dffdc3e1fb7feb7da72698f2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1475,7 +1475,7 @@ instance hasSmul' : SMul (α →ᵇ 𝕜) (α →ᵇ β) :=
   ⟨fun (f : α →ᵇ 𝕜) (g : α →ᵇ β) =>
     ofNormedAddCommGroup (fun x => f x • g x) (f.Continuous.smul g.Continuous) (‖f‖ * ‖g‖) fun x =>
       calc
-        ‖f x • g x‖ ≤ ‖f x‖ * ‖g x‖ := NormedSpace.norm_smul_le _ _
+        ‖f x • g x‖ ≤ ‖f x‖ * ‖g x‖ := norm_smul_le _ _
         _ ≤ ‖f‖ * ‖g‖ :=
           mul_le_mul (f.norm_coe_le_norm _) (g.norm_coe_le_norm _) (norm_nonneg _) (norm_nonneg _)
         ⟩

mathlib commit https://github.com/leanprover-community/mathlib/commit/da3fc4a33ff6bc75f077f691dc94c217b8d41559

@@ -1115,7 +1115,7 @@ theorem norm_compContinuous_le [TopologicalSpace γ] (f : α →ᵇ β) (g : C(
 
 end NormedAddCommGroup
 
-section BoundedSmul
+section BoundedSMul
 
 /-!
 ### `has_bounded_smul` (in particular, topological module) structure
@@ -1131,7 +1131,7 @@ variable {𝕜 : Type _} [PseudoMetricSpace 𝕜] [TopologicalSpace α] [PseudoM
 
 section SMul
 
-variable [Zero 𝕜] [Zero β] [SMul 𝕜 β] [BoundedSmul 𝕜 β]
+variable [Zero 𝕜] [Zero β] [SMul 𝕜 β] [BoundedSMul 𝕜 β]
 
 instance : SMul 𝕜 (α →ᵇ β)
     where smul c f :=
@@ -1156,7 +1156,7 @@ theorem smul_apply (c : 𝕜) (f : α →ᵇ β) (x : α) : (c • f) x = c •
 instance [SMul 𝕜ᵐᵒᵖ β] [IsCentralScalar 𝕜 β] : IsCentralScalar 𝕜 (α →ᵇ β)
     where op_smul_eq_smul _ _ := ext fun _ => op_smul_eq_smul _ _
 
-instance : BoundedSmul 𝕜 (α →ᵇ β)
+instance : BoundedSMul 𝕜 (α →ᵇ β)
     where
   dist_smul_pair' c f₁ f₂ :=
     by
@@ -1176,7 +1176,7 @@ end SMul
 
 section MulAction
 
-variable [MonoidWithZero 𝕜] [Zero β] [MulAction 𝕜 β] [BoundedSmul 𝕜 β]
+variable [MonoidWithZero 𝕜] [Zero β] [MulAction 𝕜 β] [BoundedSMul 𝕜 β]
 
 instance : MulAction 𝕜 (α →ᵇ β) :=
   FunLike.coe_injective.MulAction _ coe_smul
@@ -1185,7 +1185,7 @@ end MulAction
 
 section DistribMulAction
 
-variable [MonoidWithZero 𝕜] [AddMonoid β] [DistribMulAction 𝕜 β] [BoundedSmul 𝕜 β]
+variable [MonoidWithZero 𝕜] [AddMonoid β] [DistribMulAction 𝕜 β] [BoundedSMul 𝕜 β]
 
 variable [LipschitzAdd β]
 
@@ -1196,7 +1196,7 @@ end DistribMulAction
 
 section Module
 
-variable [Semiring 𝕜] [AddCommMonoid β] [Module 𝕜 β] [BoundedSmul 𝕜 β]
+variable [Semiring 𝕜] [AddCommMonoid β] [Module 𝕜 β] [BoundedSMul 𝕜 β]
 
 variable {f g : α →ᵇ β} {x : α} {C : ℝ}
 
@@ -1232,7 +1232,7 @@ def toContinuousMapLinearMap : (α →ᵇ β) →ₗ[𝕜] C(α, β)
 
 end Module
 
-end BoundedSmul
+end BoundedSMul
 
 section NormedSpace
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931

@@ -1305,7 +1305,7 @@ section NonUnital
 
 section SemiNormed
 
-variable [NonUnitalSemiNormedRing R]
+variable [NonUnitalSeminormedRing R]
 
 instance : Mul (α →ᵇ R)
     where mul f g :=
@@ -1326,7 +1326,7 @@ instance : NonUnitalRing (α →ᵇ R) :=
   FunLike.coe_injective.NonUnitalRing _ coe_zero coe_add coe_mul coe_neg coe_sub
     (fun _ _ => coe_nsmul _ _) fun _ _ => coe_zsmul _ _
 
-instance : NonUnitalSemiNormedRing (α →ᵇ R) :=
+instance : NonUnitalSeminormedRing (α →ᵇ R) :=
   { BoundedContinuousFunction.seminormedAddCommGroup with
     norm_mul := fun f g =>
       norm_ofNormedAddCommGroup_le _ (mul_nonneg (norm_nonneg _) (norm_nonneg _)) _ }
@@ -1341,7 +1341,7 @@ end NonUnital
 
 section SemiNormed
 
-variable [SemiNormedRing R]
+variable [SeminormedRing R]
 
 @[simp]
 theorem coe_npowRec (f : α →ᵇ R) : ∀ n, ⇑(npowRec n f) = f ^ n
@@ -1386,7 +1386,7 @@ instance : Ring (α →ᵇ R) :=
     (fun _ _ => coe_nsmul _ _) (fun _ _ => coe_zsmul _ _) (fun _ _ => coe_pow _ _) coe_nat_cast
     coe_int_cast
 
-instance : SemiNormedRing (α →ᵇ R) :=
+instance : SeminormedRing (α →ᵇ R) :=
   { BoundedContinuousFunction.nonUnitalSemiNormedRing with }
 
 end SemiNormed
@@ -1408,10 +1408,10 @@ pointwise operations and checking that they are compatible with the uniform dist
 
 variable [TopologicalSpace α] {R : Type _}
 
-instance [SemiNormedCommRing R] : CommRing (α →ᵇ R) :=
+instance [SeminormedCommRing R] : CommRing (α →ᵇ R) :=
   { BoundedContinuousFunction.ring with mul_comm := fun f₁ f₂ => ext fun x => mul_comm _ _ }
 
-instance [SemiNormedCommRing R] : SemiNormedCommRing (α →ᵇ R) :=
+instance [SeminormedCommRing R] : SeminormedCommRing (α →ᵇ R) :=
   { BoundedContinuousFunction.commRing, BoundedContinuousFunction.seminormedAddCommGroup with }
 
 instance [NormedCommRing R] : NormedCommRing (α →ᵇ R) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936

@@ -838,7 +838,7 @@ variable [TopologicalSpace α] [SeminormedAddCommGroup β]
 
 variable (f g : α →ᵇ β) {x : α} {C : ℝ}
 
-instance : HasNorm (α →ᵇ β) :=
+instance : Norm (α →ᵇ β) :=
   ⟨fun u => dist u 0⟩
 
 theorem norm_def : ‖f‖ = dist f 0 :=
@@ -1684,7 +1684,7 @@ def nnnorm (f : α →ᵇ ℝ) : α →ᵇ ℝ≥0 :=
 #align bounded_continuous_function.nnnorm BoundedContinuousFunction.nnnorm
 
 @[simp]
-theorem nnnorm_coe_fun_eq (f : α →ᵇ ℝ) : ⇑f.nnnorm = HasNnnorm.nnnorm ∘ ⇑f :=
+theorem nnnorm_coe_fun_eq (f : α →ᵇ ℝ) : ⇑f.nnnorm = NNNorm.nnnorm ∘ ⇑f :=
   rfl
 #align bounded_continuous_function.nnnorm_coe_fun_eq BoundedContinuousFunction.nnnorm_coe_fun_eq
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/3b267e70a936eebb21ab546f49a8df34dd300b25

@@ -690,7 +690,7 @@ theorem one_compContinuous [TopologicalSpace γ] (f : C(γ, α)) :
 
 end One
 
-section HasLipschitzAdd
+section LipschitzAdd
 
 /- In this section, if `β` is an `add_monoid` whose addition operation is Lipschitz, then we show
 that the space of bounded continuous functions from `α` to `β` inherits a topological `add_monoid`
@@ -704,7 +704,7 @@ trivial inconvenience, but in any case there are no obvious applications of the
 version. -/
 variable [TopologicalSpace α] [PseudoMetricSpace β] [AddMonoid β]
 
-variable [HasLipschitzAdd β]
+variable [LipschitzAdd β]
 
 variable (f g : α →ᵇ β) {x : α} {C : ℝ}
 
@@ -712,12 +712,12 @@ variable (f g : α →ᵇ β) {x : α} {C : ℝ}
 instance : Add (α →ᵇ β)
     where add f g :=
     BoundedContinuousFunction.mkOfBound (f.toContinuousMap + g.toContinuousMap)
-      (↑(HasLipschitzAdd.c β) * max (Classical.choose f.Bounded) (Classical.choose g.Bounded))
+      (↑(LipschitzAdd.C β) * max (Classical.choose f.Bounded) (Classical.choose g.Bounded))
       (by
         intro x y
         refine' le_trans (lipschitz_with_lipschitz_const_add ⟨f x, g x⟩ ⟨f y, g y⟩) _
         rw [Prod.dist_eq]
-        refine' mul_le_mul_of_nonneg_left _ (HasLipschitzAdd.c β).coe_nonneg
+        refine' mul_le_mul_of_nonneg_left _ (LipschitzAdd.C β).coe_nonneg
         apply max_le_max
         exact Classical.choose_spec f.bounded x y
         exact Classical.choose_spec g.bounded x y)
@@ -767,10 +767,10 @@ theorem nsmul_apply (r : ℕ) (f : α →ᵇ β) (v : α) : (r • f) v = r •
 instance : AddMonoid (α →ᵇ β) :=
   FunLike.coe_injective.AddMonoid _ coe_zero coe_add fun _ _ => coe_nsmul _ _
 
-instance : HasLipschitzAdd (α →ᵇ β)
+instance : LipschitzAdd (α →ᵇ β)
     where lipschitz_add :=
-    ⟨HasLipschitzAdd.c β, by
-      have C_nonneg := (HasLipschitzAdd.c β).coe_nonneg
+    ⟨LipschitzAdd.C β, by
+      have C_nonneg := (LipschitzAdd.C β).coe_nonneg
       rw [lipschitzWith_iff_dist_le_mul]
       rintro ⟨f₁, g₁⟩ ⟨f₂, g₂⟩
       rw [dist_le (mul_nonneg C_nonneg dist_nonneg)]
@@ -805,11 +805,11 @@ def toContinuousMapAddHom : (α →ᵇ β) →+ C(α, β)
     simp
 #align bounded_continuous_function.to_continuous_map_add_hom BoundedContinuousFunction.toContinuousMapAddHom
 
-end HasLipschitzAdd
+end LipschitzAdd
 
 section CommHasLipschitzAdd
 
-variable [TopologicalSpace α] [PseudoMetricSpace β] [AddCommMonoid β] [HasLipschitzAdd β]
+variable [TopologicalSpace α] [PseudoMetricSpace β] [AddCommMonoid β] [LipschitzAdd β]
 
 @[to_additive]
 instance : AddCommMonoid (α →ᵇ β) :=
@@ -1115,7 +1115,7 @@ theorem norm_compContinuous_le [TopologicalSpace γ] (f : α →ᵇ β) (g : C(
 
 end NormedAddCommGroup
 
-section HasBoundedSmul
+section BoundedSmul
 
 /-!
 ### `has_bounded_smul` (in particular, topological module) structure
@@ -1131,7 +1131,7 @@ variable {𝕜 : Type _} [PseudoMetricSpace 𝕜] [TopologicalSpace α] [PseudoM
 
 section SMul
 
-variable [Zero 𝕜] [Zero β] [SMul 𝕜 β] [HasBoundedSmul 𝕜 β]
+variable [Zero 𝕜] [Zero β] [SMul 𝕜 β] [BoundedSmul 𝕜 β]
 
 instance : SMul 𝕜 (α →ᵇ β)
     where smul c f :=
@@ -1156,7 +1156,7 @@ theorem smul_apply (c : 𝕜) (f : α →ᵇ β) (x : α) : (c • f) x = c •
 instance [SMul 𝕜ᵐᵒᵖ β] [IsCentralScalar 𝕜 β] : IsCentralScalar 𝕜 (α →ᵇ β)
     where op_smul_eq_smul _ _ := ext fun _ => op_smul_eq_smul _ _
 
-instance : HasBoundedSmul 𝕜 (α →ᵇ β)
+instance : BoundedSmul 𝕜 (α →ᵇ β)
     where
   dist_smul_pair' c f₁ f₂ :=
     by
@@ -1176,7 +1176,7 @@ end SMul
 
 section MulAction
 
-variable [MonoidWithZero 𝕜] [Zero β] [MulAction 𝕜 β] [HasBoundedSmul 𝕜 β]
+variable [MonoidWithZero 𝕜] [Zero β] [MulAction 𝕜 β] [BoundedSmul 𝕜 β]
 
 instance : MulAction 𝕜 (α →ᵇ β) :=
   FunLike.coe_injective.MulAction _ coe_smul
@@ -1185,9 +1185,9 @@ end MulAction
 
 section DistribMulAction
 
-variable [MonoidWithZero 𝕜] [AddMonoid β] [DistribMulAction 𝕜 β] [HasBoundedSmul 𝕜 β]
+variable [MonoidWithZero 𝕜] [AddMonoid β] [DistribMulAction 𝕜 β] [BoundedSmul 𝕜 β]
 
-variable [HasLipschitzAdd β]
+variable [LipschitzAdd β]
 
 instance : DistribMulAction 𝕜 (α →ᵇ β) :=
   Function.Injective.distribMulAction ⟨_, coe_zero, coe_add⟩ FunLike.coe_injective coe_smul
@@ -1196,11 +1196,11 @@ end DistribMulAction
 
 section Module
 
-variable [Semiring 𝕜] [AddCommMonoid β] [Module 𝕜 β] [HasBoundedSmul 𝕜 β]
+variable [Semiring 𝕜] [AddCommMonoid β] [Module 𝕜 β] [BoundedSmul 𝕜 β]
 
 variable {f g : α →ᵇ β} {x : α} {C : ℝ}
 
-variable [HasLipschitzAdd β]
+variable [LipschitzAdd β]
 
 instance : Module 𝕜 (α →ᵇ β) :=
   Function.Injective.module _ ⟨_, coe_zero, coe_add⟩ FunLike.coe_injective coe_smul
@@ -1232,7 +1232,7 @@ def toContinuousMapLinearMap : (α →ᵇ β) →ₗ[𝕜] C(α, β)
 
 end Module
 
-end HasBoundedSmul
+end BoundedSmul
 
 section NormedSpace
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/3b267e70a936eebb21ab546f49a8df34dd300b25

@@ -623,7 +623,7 @@ theorem arzela_ascoli₂ (s : Set β) (hs : IsCompact s) (A : Set (α →ᵇ β)
   by
   /- This version is deduced from the previous one by restricting to the compact type in the target,
   using compactness there and then lifting everything to the original space. -/
-  have M : LipschitzWith 1 coe := LipschitzWith.subtype_coe s
+  have M : LipschitzWith 1 coe := LipschitzWith.subtype_val s
   let F : (α →ᵇ s) → α →ᵇ β := comp coe M
   refine'
     isCompact_of_isClosed_subset ((_ : IsCompact (F ⁻¹' A)).image (continuous_comp M)) closed

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

@@ -159,7 +159,7 @@ def mkOfDiscrete [DiscreteTopology α] (f : α → β) (C : ℝ) (h : ∀ x y :
 #align bounded_continuous_function.mk_of_discrete BoundedContinuousFunction.mkOfDiscrete
 
 /-- The uniform distance between two bounded continuous functions -/
-instance : HasDist (α →ᵇ β) :=
+instance : Dist (α →ᵇ β) :=
   ⟨fun f g => infₛ { C | 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C }⟩
 
 theorem dist_eq : dist f g = infₛ { C | 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C } :=

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

@@ -435,7 +435,7 @@ def comp (G : β → γ) {C : ℝ≥0} (H : LipschitzWith C G) (f : α →ᵇ β
     ⟨max C 0 * D, fun x y =>
       calc
         dist (G (f x)) (G (f y)) ≤ C * dist (f x) (f y) := H.dist_le_mul _ _
-        _ ≤ max C 0 * dist (f x) (f y) := mul_le_mul_of_nonneg_right (le_max_left C 0) dist_nonneg
+        _ ≤ max C 0 * dist (f x) (f y) := (mul_le_mul_of_nonneg_right (le_max_left C 0) dist_nonneg)
         _ ≤ max C 0 * D := mul_le_mul_of_nonneg_left (hD _ _) (le_max_right C 0)
         ⟩⟩
 #align bounded_continuous_function.comp BoundedContinuousFunction.comp
@@ -516,7 +516,7 @@ theorem dist_extend_extend (f : α ↪ δ) (g₁ g₂ : α →ᵇ β) (h₁ h₂
       lift x to (range fᶜ : Set δ) using hx
       calc
         dist (h₁ x) (h₂ x) = dist (h₁.restrict (range fᶜ) x) (h₂.restrict (range fᶜ) x) := rfl
-        _ ≤ dist (h₁.restrict (range fᶜ)) (h₂.restrict (range fᶜ)) := dist_coe_le_dist x
+        _ ≤ dist (h₁.restrict (range fᶜ)) (h₂.restrict (range fᶜ)) := (dist_coe_le_dist x)
         _ ≤ _ := le_max_right _ _
         
   · refine' (dist_le dist_nonneg).2 fun x => _
@@ -544,7 +544,7 @@ variable [TopologicalSpace α] [CompactSpace α] [PseudoMetricSpace β]
 
 variable {f g : α →ᵇ β} {x : α} {C : ℝ}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (y z «expr ∈ » U) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y z «expr ∈ » U) -/
 /- Arzela-Ascoli theorem asserts that, on a compact space, a set of functions sharing
 a common modulus of continuity and taking values in a compact set forms a compact
 subset for the topology of uniform convergence. In this section, we prove this theorem
@@ -600,7 +600,7 @@ theorem arzela_ascoli₁ [CompactSpace β] (A : Set (α →ᵇ β)) (closed : Is
   calc
     dist (f x) (g x) ≤ dist (f x) (f x') + dist (g x) (g x') + dist (f x') (g x') :=
       dist_triangle4_right _ _ _ _
-    _ ≤ ε₂ + ε₂ + ε₁ / 2 := le_of_lt (add_lt_add (add_lt_add _ _) _)
+    _ ≤ ε₂ + ε₂ + ε₁ / 2 := (le_of_lt (add_lt_add (add_lt_add _ _) _))
     _ = ε₁ := by rw [add_halves, add_halves]
     
   · exact (hU x').2.2 _ hx' _ (hU x').1 hf
@@ -611,7 +611,7 @@ theorem arzela_ascoli₁ [CompactSpace β] (A : Set (α →ᵇ β)) (closed : Is
       dist (f x') (g x') ≤ dist (f x') (F (f x')) + dist (g x') (F (f x')) :=
         dist_triangle_right _ _ _
       _ = dist (f x') (F (f x')) + dist (g x') (F (g x')) := by rw [F_f_g]
-      _ < ε₂ + ε₂ := add_lt_add (hF (f x')).2 (hF (g x')).2
+      _ < ε₂ + ε₂ := (add_lt_add (hF (f x')).2 (hF (g x')).2)
       _ = ε₁ / 2 := add_halves _
       
 #align bounded_continuous_function.arzela_ascoli₁ BoundedContinuousFunction.arzela_ascoli₁
@@ -879,7 +879,7 @@ theorem dist_le_two_norm' {f : γ → β} {C : ℝ} (hC : ∀ x, ‖f x‖ ≤ C
     dist (f x) (f y) ≤ 2 * C :=
   calc
     dist (f x) (f y) ≤ ‖f x‖ + ‖f y‖ := dist_le_norm_add_norm _ _
-    _ ≤ C + C := add_le_add (hC x) (hC y)
+    _ ≤ C + C := (add_le_add (hC x) (hC y))
     _ = 2 * C := (two_mul _).symm
     
 #align bounded_continuous_function.dist_le_two_norm' BoundedContinuousFunction.dist_le_two_norm'

mathlib commit https://github.com/leanprover-community/mathlib/commit/22131150f88a2d125713ffa0f4693e3355b1eb49

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Mario Carneiro, Yury Kudryashov, Heather Macbeth
 
 ! This file was ported from Lean 3 source module topology.continuous_function.bounded
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 6efec6bb9fcaed3cf1baaddb2eaadd8a2a06679c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -384,13 +384,24 @@ instance [CompleteSpace β] : CompleteSpace (α →ᵇ β) :=
       exact fun N => (dist_le (b0 _)).2 fun x => fF_bdd x N
 
 /-- Composition of a bounded continuous function and a continuous function. -/
-@[simps (config := { fullyApplied := false })]
 def compContinuous {δ : Type _} [TopologicalSpace δ] (f : α →ᵇ β) (g : C(δ, α)) : δ →ᵇ β
     where
   toContinuousMap := f.1.comp g
   map_bounded' := f.map_bounded'.imp fun C hC x y => hC _ _
 #align bounded_continuous_function.comp_continuous BoundedContinuousFunction.compContinuous
 
+@[simp]
+theorem coe_compContinuous {δ : Type _} [TopologicalSpace δ] (f : α →ᵇ β) (g : C(δ, α)) :
+    coeFn (f.comp_continuous g) = f ∘ g :=
+  rfl
+#align bounded_continuous_function.coe_comp_continuous BoundedContinuousFunction.coe_compContinuous
+
+@[simp]
+theorem compContinuous_apply {δ : Type _} [TopologicalSpace δ] (f : α →ᵇ β) (g : C(δ, α)) (x : δ) :
+    f.comp_continuous g x = f (g x) :=
+  rfl
+#align bounded_continuous_function.comp_continuous_apply BoundedContinuousFunction.compContinuous_apply
+
 theorem lipschitz_compContinuous {δ : Type _} [TopologicalSpace δ] (g : C(δ, α)) :
     LipschitzWith 1 fun f : α →ᵇ β => f.comp_continuous g :=
   LipschitzWith.mk_one fun f₁ f₂ => (dist_le dist_nonneg).2 fun x => dist_coe_le_dist (g x)
@@ -402,11 +413,20 @@ theorem continuous_compContinuous {δ : Type _} [TopologicalSpace δ] (g : C(δ,
 #align bounded_continuous_function.continuous_comp_continuous BoundedContinuousFunction.continuous_compContinuous
 
 /-- Restrict a bounded continuous function to a set. -/
-@[simps (config := { fullyApplied := false }) apply]
 def restrict (f : α →ᵇ β) (s : Set α) : s →ᵇ β :=
   f.comp_continuous <| (ContinuousMap.id _).restrict s
 #align bounded_continuous_function.restrict BoundedContinuousFunction.restrict
 
+@[simp]
+theorem coe_restrict (f : α →ᵇ β) (s : Set α) : coeFn (f.restrict s) = f ∘ coe :=
+  rfl
+#align bounded_continuous_function.coe_restrict BoundedContinuousFunction.coe_restrict
+
+@[simp]
+theorem restrict_apply (f : α →ᵇ β) (s : Set α) (x : s) : f.restrict s x = f x :=
+  rfl
+#align bounded_continuous_function.restrict_apply BoundedContinuousFunction.restrict_apply
+
 /-- Composition (in the target) of a bounded continuous function with a Lipschitz map again
 gives a bounded continuous function -/
 def comp (G : β → γ) {C : ℝ≥0} (H : LipschitzWith C G) (f : α →ᵇ β) : α →ᵇ γ :=

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

A PR accompanying #12339.

Zulip discussion

@@ -668,8 +668,8 @@ instance instAdd : Add (α →ᵇ β) where
         rw [Prod.dist_eq]
         refine' mul_le_mul_of_nonneg_left _ (LipschitzAdd.C β).coe_nonneg
         apply max_le_max
-        exact Classical.choose_spec f.bounded x y
-        exact Classical.choose_spec g.bounded x y)
+        · exact Classical.choose_spec f.bounded x y
+        · exact Classical.choose_spec g.bounded x y)
 
 @[simp]
 theorem coe_add : ⇑(f + g) = f + g := rfl

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

@@ -485,7 +485,7 @@ theorem dist_extend_extend (f : α ↪ δ) (g₁ g₂ : α →ᵇ β) (h₁ h₂
       lift x to ((range f)ᶜ : Set δ) using hx
       calc
         dist (h₁ x) (h₂ x) = dist (h₁.restrict (range f)ᶜ x) (h₂.restrict (range f)ᶜ x) := rfl
-        _ ≤ dist (h₁.restrict (range f)ᶜ) (h₂.restrict (range f)ᶜ) := (dist_coe_le_dist x)
+        _ ≤ dist (h₁.restrict (range f)ᶜ) (h₂.restrict (range f)ᶜ) := dist_coe_le_dist x
         _ ≤ _ := le_max_right _ _
   · refine' (dist_le dist_nonneg).2 fun x => _
     rw [← extend_apply f g₁ h₁, ← extend_apply f g₂ h₂]
@@ -818,7 +818,7 @@ theorem dist_le_two_norm' {f : γ → β} {C : ℝ} (hC : ∀ x, ‖f x‖ ≤ C
     dist (f x) (f y) ≤ 2 * C :=
   calc
     dist (f x) (f y) ≤ ‖f x‖ + ‖f y‖ := dist_le_norm_add_norm _ _
-    _ ≤ C + C := (add_le_add (hC x) (hC y))
+    _ ≤ C + C := add_le_add (hC x) (hC y)
     _ = 2 * C := (two_mul _).symm
 #align bounded_continuous_function.dist_le_two_norm' BoundedContinuousFunction.dist_le_two_norm'
 

Quoting [@digama0](https://github.com/digama0):

These were actually never meant to go in the file, they are basically debugging information and only useful on significantly broken mathport files. You can safely remove all of them.

@@ -44,7 +44,6 @@ structure BoundedContinuousFunction (α : Type u) (β : Type v) [TopologicalSpac
   map_bounded' : ∃ C, ∀ x y, dist (toFun x) (toFun y) ≤ C
 #align bounded_continuous_function BoundedContinuousFunction
 
--- mathport name: bounded_continuous_function
 scoped[BoundedContinuousFunction] infixr:25 " →ᵇ " => BoundedContinuousFunction
 
 section

It's annoying that zsmulRec uses nsmulRec to define zsmul even when the user already set nsmul explicitly. This PR changes zsmulRec to take nsmul as an argument.

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

@@ -961,15 +961,15 @@ theorem mkOfCompact_sub [CompactSpace α] (f g : C(α, β)) :
 #align bounded_continuous_function.mk_of_compact_sub BoundedContinuousFunction.mkOfCompact_sub
 
 @[simp]
-theorem coe_zsmulRec : ∀ z, ⇑(zsmulRec z f) = z • ⇑f
-  | Int.ofNat n => by rw [zsmulRec, Int.ofNat_eq_coe, coe_nsmulRec, natCast_zsmul]
-  | Int.negSucc n => by rw [zsmulRec, negSucc_zsmul, coe_neg, coe_nsmulRec]
+theorem coe_zsmulRec : ∀ z, ⇑(zsmulRec (· • ·) z f) = z • ⇑f
+  | Int.ofNat n => by rw [zsmulRec, Int.ofNat_eq_coe, coe_nsmul, natCast_zsmul]
+  | Int.negSucc n => by rw [zsmulRec, negSucc_zsmul, coe_neg, coe_nsmul]
 #align bounded_continuous_function.coe_zsmul_rec BoundedContinuousFunction.coe_zsmulRec
 
 instance instSMulInt : SMul ℤ (α →ᵇ β) where
   smul n f :=
     { toContinuousMap := n • f.toContinuousMap
-      map_bounded' := by simpa using (zsmulRec n f).map_bounded' }
+      map_bounded' := by simpa using (zsmulRec (· • ·) n f).map_bounded' }
 #align bounded_continuous_function.has_int_scalar BoundedContinuousFunction.instSMulInt
 
 @[simp]

... and add a deprecated alias for the old name. This is mostly just me discovering the power of F2

@@ -962,7 +962,7 @@ theorem mkOfCompact_sub [CompactSpace α] (f g : C(α, β)) :
 
 @[simp]
 theorem coe_zsmulRec : ∀ z, ⇑(zsmulRec z f) = z • ⇑f
-  | Int.ofNat n => by rw [zsmulRec, Int.ofNat_eq_coe, coe_nsmulRec, coe_nat_zsmul]
+  | Int.ofNat n => by rw [zsmulRec, Int.ofNat_eq_coe, coe_nsmulRec, natCast_zsmul]
   | Int.negSucc n => by rw [zsmulRec, negSucc_zsmul, coe_neg, coe_nsmulRec]
 #align bounded_continuous_function.coe_zsmul_rec BoundedContinuousFunction.coe_zsmulRec
 

All the unnamed instances here were very long, and Moritz recently linked one of these to a newcomer.

Also slightly clean up the Lattice instance

@@ -69,18 +69,18 @@ section Basics
 variable [TopologicalSpace α] [PseudoMetricSpace β] [PseudoMetricSpace γ]
 variable {f g : α →ᵇ β} {x : α} {C : ℝ}
 
-instance : FunLike (α →ᵇ β) α β where
+instance instFunLike : FunLike (α →ᵇ β) α β where
   coe f := f.toFun
   coe_injective' f g h := by
     obtain ⟨⟨_, _⟩, _⟩ := f
     obtain ⟨⟨_, _⟩, _⟩ := g
     congr
 
-instance : BoundedContinuousMapClass (α →ᵇ β) α β where
+instance instBoundedContinuousMapClass : BoundedContinuousMapClass (α →ᵇ β) α β where
   map_continuous f := f.continuous_toFun
   map_bounded f := f.map_bounded'
 
-instance [FunLike F α β] [BoundedContinuousMapClass F α β] : CoeTC F (α →ᵇ β) :=
+instance instCoeTC [FunLike F α β] [BoundedContinuousMapClass F α β] : CoeTC F (α →ᵇ β) :=
   ⟨fun f =>
     { toFun := f
       continuous_toFun := map_continuous f
@@ -149,7 +149,7 @@ def mkOfDiscrete [DiscreteTopology α] (f : α → β) (C : ℝ) (h : ∀ x y :
 #align bounded_continuous_function.mk_of_discrete BoundedContinuousFunction.mkOfDiscrete
 
 /-- The uniform distance between two bounded continuous functions. -/
-instance : Dist (α →ᵇ β) :=
+instance instDist : Dist (α →ᵇ β) :=
   ⟨fun f g => sInf { C | 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C }⟩
 
 theorem dist_eq : dist f g = sInf { C | 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C } := rfl
@@ -211,7 +211,7 @@ theorem dist_lt_iff_of_nonempty_compact [Nonempty α] [CompactSpace α] :
 #align bounded_continuous_function.dist_lt_iff_of_nonempty_compact BoundedContinuousFunction.dist_lt_iff_of_nonempty_compact
 
 /-- The type of bounded continuous functions, with the uniform distance, is a pseudometric space. -/
-instance : PseudoMetricSpace (α →ᵇ β) where
+instance instPseudoMetricSpace : PseudoMetricSpace (α →ᵇ β) where
   dist_self f := le_antisymm ((dist_le le_rfl).2 fun x => by simp) dist_nonneg'
   dist_comm f g := by simp [dist_eq, dist_comm]
   dist_triangle f g h := (dist_le (add_nonneg dist_nonneg' dist_nonneg')).2
@@ -220,7 +220,7 @@ instance : PseudoMetricSpace (α →ᵇ β) where
   edist_dist x y := by dsimp; congr; simp [dist_nonneg']
 
 /-- The type of bounded continuous functions, with the uniform distance, is a metric space. -/
-instance {α β} [TopologicalSpace α] [MetricSpace β] : MetricSpace (α →ᵇ β) where
+instance instMetricSpace {β} [MetricSpace β] : MetricSpace (α →ᵇ β) where
   eq_of_dist_eq_zero hfg := by
     ext x
     exact eq_of_dist_eq_zero (le_antisymm (hfg ▸ dist_coe_le_dist _) dist_nonneg)
@@ -327,7 +327,7 @@ theorem continuous_eval : Continuous fun p : (α →ᵇ β) × α => p.1 p.2 :=
 #align bounded_continuous_function.continuous_eval BoundedContinuousFunction.continuous_eval
 
 /-- Bounded continuous functions taking values in a complete space form a complete space. -/
-instance [CompleteSpace β] : CompleteSpace (α →ᵇ β) :=
+instance instCompleteSpace [CompleteSpace β] : CompleteSpace (α →ᵇ β) :=
   complete_of_cauchySeq_tendsto fun (f : ℕ → α →ᵇ β) (hf : CauchySeq f) => by
     /- We have to show that `f n` converges to a bounded continuous function.
       For this, we prove pointwise convergence to define the limit, then check
@@ -616,9 +616,7 @@ section One
 
 variable [TopologicalSpace α] [PseudoMetricSpace β] [One β]
 
-@[to_additive]
-instance : One (α →ᵇ β) :=
-  ⟨const α 1⟩
+@[to_additive] instance instOne : One (α →ᵇ β) := ⟨const α 1⟩
 
 @[to_additive (attr := simp)]
 theorem coe_one : ((1 : α →ᵇ β) : α → β) = 1 := rfl
@@ -661,7 +659,7 @@ variable [LipschitzAdd β]
 variable (f g : α →ᵇ β) {x : α} {C : ℝ}
 
 /-- The pointwise sum of two bounded continuous functions is again bounded continuous. -/
-instance : Add (α →ᵇ β) where
+instance instAdd : Add (α →ᵇ β) where
   add f g :=
     BoundedContinuousFunction.mkOfBound (f.toContinuousMap + g.toContinuousMap)
       (↑(LipschitzAdd.C β) * max (Classical.choose f.bounded) (Classical.choose g.bounded))
@@ -696,11 +694,11 @@ theorem coe_nsmulRec : ∀ n, ⇑(nsmulRec n f) = n • ⇑f
   | n + 1 => by rw [nsmulRec, succ_nsmul, coe_add, coe_nsmulRec n]
 #align bounded_continuous_function.coe_nsmul_rec BoundedContinuousFunction.coe_nsmulRec
 
-instance hasNatScalar : SMul ℕ (α →ᵇ β) where
+instance instSMulNat : SMul ℕ (α →ᵇ β) where
   smul n f :=
     { toContinuousMap := n • f.toContinuousMap
       map_bounded' := by simpa [coe_nsmulRec] using (nsmulRec n f).map_bounded' }
-#align bounded_continuous_function.has_nat_scalar BoundedContinuousFunction.hasNatScalar
+#align bounded_continuous_function.has_nat_scalar BoundedContinuousFunction.instSMulNat
 
 @[simp]
 theorem coe_nsmul (r : ℕ) (f : α →ᵇ β) : ⇑(r • f) = r • ⇑f := rfl
@@ -710,10 +708,10 @@ theorem coe_nsmul (r : ℕ) (f : α →ᵇ β) : ⇑(r • f) = r • ⇑f := rf
 theorem nsmul_apply (r : ℕ) (f : α →ᵇ β) (v : α) : (r • f) v = r • f v := rfl
 #align bounded_continuous_function.nsmul_apply BoundedContinuousFunction.nsmul_apply
 
-instance addMonoid : AddMonoid (α →ᵇ β) :=
+instance instAddMonoid : AddMonoid (α →ᵇ β) :=
   DFunLike.coe_injective.addMonoid _ coe_zero coe_add fun _ _ => coe_nsmul _ _
 
-instance : LipschitzAdd (α →ᵇ β) where
+instance instLipschitzAdd : LipschitzAdd (α →ᵇ β) where
   lipschitz_add :=
     ⟨LipschitzAdd.C β, by
       have C_nonneg := (LipschitzAdd.C β).coe_nonneg
@@ -753,9 +751,8 @@ section CommHasLipschitzAdd
 variable [TopologicalSpace α] [PseudoMetricSpace β] [AddCommMonoid β] [LipschitzAdd β]
 
 @[to_additive]
-instance : AddCommMonoid (α →ᵇ β) :=
-  { BoundedContinuousFunction.addMonoid with
-    add_comm := fun f g => by ext; simp [add_comm] }
+instance instAddCommMonoid : AddCommMonoid (α →ᵇ β) where
+  add_comm f g := by ext; simp [add_comm]
 
 open BigOperators
 
@@ -779,8 +776,7 @@ pointwise operations and checking that they are compatible with the uniform dist
 variable [TopologicalSpace α] [SeminormedAddCommGroup β]
 variable (f g : α →ᵇ β) {x : α} {C : ℝ}
 
-instance : Norm (α →ᵇ β) :=
-  ⟨fun u => dist u 0⟩
+instance instNorm : Norm (α →ᵇ β) := ⟨(dist · 0)⟩
 
 theorem norm_def : ‖f‖ = dist f 0 := rfl
 #align bounded_continuous_function.norm_def BoundedContinuousFunction.norm_def
@@ -924,7 +920,7 @@ theorem norm_eq_iSup_norm : ‖f‖ = ⨆ x : α, ‖f x‖ := by
 #align bounded_continuous_function.norm_eq_supr_norm BoundedContinuousFunction.norm_eq_iSup_norm
 
 /-- If `‖(1 : β)‖ = 1`, then `‖(1 : α →ᵇ β)‖ = 1` if `α` is nonempty. -/
-instance [Nonempty α] [One β] [NormOneClass β] : NormOneClass (α →ᵇ β) where
+instance instNormOneClass [Nonempty α] [One β] [NormOneClass β] : NormOneClass (α →ᵇ β) where
   norm_one := by simp only [norm_eq_iSup_norm, coe_one, Pi.one_apply, norm_one, ciSup_const]
 
 /-- The pointwise opposite of a bounded continuous function is again bounded continuous. -/
@@ -934,7 +930,7 @@ instance : Neg (α →ᵇ β) :=
       norm_neg ((⇑f) x) ▸ f.norm_coe_le_norm x⟩
 
 /-- The pointwise difference of two bounded continuous functions is again bounded continuous. -/
-instance : Sub (α →ᵇ β) :=
+instance instSub : Sub (α →ᵇ β) :=
   ⟨fun f g =>
     ofNormedAddCommGroup (f - g) (f.continuous.sub g.continuous) (‖f‖ + ‖g‖) fun x => by
       simp only [sub_eq_add_neg]
@@ -970,11 +966,11 @@ theorem coe_zsmulRec : ∀ z, ⇑(zsmulRec z f) = z • ⇑f
   | Int.negSucc n => by rw [zsmulRec, negSucc_zsmul, coe_neg, coe_nsmulRec]
 #align bounded_continuous_function.coe_zsmul_rec BoundedContinuousFunction.coe_zsmulRec
 
-instance hasIntScalar : SMul ℤ (α →ᵇ β) where
+instance instSMulInt : SMul ℤ (α →ᵇ β) where
   smul n f :=
     { toContinuousMap := n • f.toContinuousMap
       map_bounded' := by simpa using (zsmulRec n f).map_bounded' }
-#align bounded_continuous_function.has_int_scalar BoundedContinuousFunction.hasIntScalar
+#align bounded_continuous_function.has_int_scalar BoundedContinuousFunction.instSMulInt
 
 @[simp]
 theorem coe_zsmul (r : ℤ) (f : α →ᵇ β) : ⇑(r • f) = r • ⇑f := rfl
@@ -984,17 +980,17 @@ theorem coe_zsmul (r : ℤ) (f : α →ᵇ β) : ⇑(r • f) = r • ⇑f := rf
 theorem zsmul_apply (r : ℤ) (f : α →ᵇ β) (v : α) : (r • f) v = r • f v := rfl
 #align bounded_continuous_function.zsmul_apply BoundedContinuousFunction.zsmul_apply
 
-instance : AddCommGroup (α →ᵇ β) :=
+instance instAddCommGroup : AddCommGroup (α →ᵇ β) :=
   DFunLike.coe_injective.addCommGroup _ coe_zero coe_add coe_neg coe_sub (fun _ _ => coe_nsmul _ _)
     fun _ _ => coe_zsmul _ _
 
-instance seminormedAddCommGroup : SeminormedAddCommGroup (α →ᵇ β) where
+instance instSeminormedAddCommGroup : SeminormedAddCommGroup (α →ᵇ β) where
   dist_eq f g := by simp only [norm_eq, dist_eq, dist_eq_norm, sub_apply]
 
-instance normedAddCommGroup {α β} [TopologicalSpace α] [NormedAddCommGroup β] :
+instance instNormedAddCommGroup {α β} [TopologicalSpace α] [NormedAddCommGroup β] :
     NormedAddCommGroup (α →ᵇ β) :=
-  { BoundedContinuousFunction.seminormedAddCommGroup with
-    -- Porting note (#10888): added proof for `eq_of_dist_eq_zero`
+  { instSeminormedAddCommGroup with
+    -- Porting note (#10888): Added a proof for `eq_of_dist_eq_zero`
     eq_of_dist_eq_zero }
 
 theorem nnnorm_def : ‖f‖₊ = nndist f 0 := rfl
@@ -1061,7 +1057,7 @@ section SMul
 
 variable [Zero 𝕜] [Zero β] [SMul 𝕜 β] [BoundedSMul 𝕜 β]
 
-instance : SMul 𝕜 (α →ᵇ β) where
+instance instSMul : SMul 𝕜 (α →ᵇ β) where
   smul c f :=
     { toContinuousMap := c • f.toContinuousMap
       map_bounded' :=
@@ -1078,10 +1074,10 @@ theorem coe_smul (c : 𝕜) (f : α →ᵇ β) : ⇑(c • f) = fun x => c • f
 theorem smul_apply (c : 𝕜) (f : α →ᵇ β) (x : α) : (c • f) x = c • f x := rfl
 #align bounded_continuous_function.smul_apply BoundedContinuousFunction.smul_apply
 
-instance [SMul 𝕜ᵐᵒᵖ β] [IsCentralScalar 𝕜 β] : IsCentralScalar 𝕜 (α →ᵇ β) where
+instance instIsCentralScalar [SMul 𝕜ᵐᵒᵖ β] [IsCentralScalar 𝕜 β] : IsCentralScalar 𝕜 (α →ᵇ β) where
   op_smul_eq_smul _ _ := ext fun _ => op_smul_eq_smul _ _
 
-instance : BoundedSMul 𝕜 (α →ᵇ β) where
+instance instBoundedSMul : BoundedSMul 𝕜 (α →ᵇ β) where
   dist_smul_pair' c f₁ f₂ := by
     rw [dist_le (mul_nonneg dist_nonneg dist_nonneg)]
     intro x
@@ -1101,7 +1097,7 @@ section MulAction
 
 variable [MonoidWithZero 𝕜] [Zero β] [MulAction 𝕜 β] [BoundedSMul 𝕜 β]
 
-instance : MulAction 𝕜 (α →ᵇ β) :=
+instance instMulAction : MulAction 𝕜 (α →ᵇ β) :=
   DFunLike.coe_injective.mulAction _ coe_smul
 
 end MulAction
@@ -1111,8 +1107,8 @@ section DistribMulAction
 variable [MonoidWithZero 𝕜] [AddMonoid β] [DistribMulAction 𝕜 β] [BoundedSMul 𝕜 β]
 variable [LipschitzAdd β]
 
-instance : DistribMulAction 𝕜 (α →ᵇ β) :=
-  Function.Injective.distribMulAction ⟨⟨_, coe_zero⟩, coe_add⟩ DFunLike.coe_injective coe_smul
+instance instDistribMulAction : DistribMulAction 𝕜 (α →ᵇ β) :=
+  DFunLike.coe_injective.distribMulAction ⟨⟨_, coe_zero⟩, coe_add⟩ coe_smul
 
 end DistribMulAction
 
@@ -1122,8 +1118,8 @@ variable [Semiring 𝕜] [AddCommMonoid β] [Module 𝕜 β] [BoundedSMul 𝕜 
 variable {f g : α →ᵇ β} {x : α} {C : ℝ}
 variable [LipschitzAdd β]
 
-instance module : Module 𝕜 (α →ᵇ β) :=
-  Function.Injective.module _ ⟨⟨_, coe_zero⟩, coe_add⟩ DFunLike.coe_injective coe_smul
+instance instModule : Module 𝕜 (α →ᵇ β) :=
+  DFunLike.coe_injective.module _ ⟨⟨_, coe_zero⟩, coe_add⟩  coe_smul
 
 variable (𝕜)
 
@@ -1166,7 +1162,7 @@ variable {𝕜 : Type*}
 variable [TopologicalSpace α] [SeminormedAddCommGroup β]
 variable {f g : α →ᵇ β} {x : α} {C : ℝ}
 
-instance normedSpace [NormedField 𝕜] [NormedSpace 𝕜 β] : NormedSpace 𝕜 (α →ᵇ β) :=
+instance instNormedSpace [NormedField 𝕜] [NormedSpace 𝕜 β] : NormedSpace 𝕜 (α →ᵇ β) :=
   ⟨fun c f => by
     refine' norm_ofNormedAddCommGroup_le _ (mul_nonneg (norm_nonneg _) (norm_nonneg _)) _
     exact fun x =>
@@ -1217,7 +1213,7 @@ section Seminormed
 
 variable [NonUnitalSeminormedRing R]
 
-instance : Mul (α →ᵇ R) where
+instance instMul : Mul (α →ᵇ R) where
   mul f g :=
     ofNormedAddCommGroup (f * g) (f.continuous.mul g.continuous) (‖f‖ * ‖g‖) fun x =>
       le_trans (norm_mul_le (f x) (g x)) <|
@@ -1230,12 +1226,12 @@ theorem coe_mul (f g : α →ᵇ R) : ⇑(f * g) = f * g := rfl
 theorem mul_apply (f g : α →ᵇ R) (x : α) : (f * g) x = f x * g x := rfl
 #align bounded_continuous_function.mul_apply BoundedContinuousFunction.mul_apply
 
-instance : NonUnitalRing (α →ᵇ R) :=
+instance instNonUnitalRing : NonUnitalRing (α →ᵇ R) :=
   DFunLike.coe_injective.nonUnitalRing _ coe_zero coe_add coe_mul coe_neg coe_sub
     (fun _ _ => coe_nsmul _ _) fun _ _ => coe_zsmul _ _
 
-instance nonUnitalSeminormedRing : NonUnitalSeminormedRing (α →ᵇ R) :=
-  { BoundedContinuousFunction.seminormedAddCommGroup with
+instance instNonUnitalSeminormedRing : NonUnitalSeminormedRing (α →ᵇ R) :=
+  { instSeminormedAddCommGroup with
     norm_mul := fun _ _ =>
       norm_ofNormedAddCommGroup_le _ (mul_nonneg (norm_nonneg _) (norm_nonneg _)) _
     -- Porting note: These 5 fields were missing. Add them.
@@ -1243,9 +1239,9 @@ instance nonUnitalSeminormedRing : NonUnitalSeminormedRing (α →ᵇ R) :=
 
 end Seminormed
 
-instance nonUnitalNormedRing [NonUnitalNormedRing R] : NonUnitalNormedRing (α →ᵇ R) :=
-  { BoundedContinuousFunction.nonUnitalSeminormedRing,
-    BoundedContinuousFunction.normedAddCommGroup with }
+instance instNonUnitalNormedRing [NonUnitalNormedRing R] : NonUnitalNormedRing (α →ᵇ R) where
+  __ := instNonUnitalSeminormedRing
+  __ := instNormedAddCommGroup
 
 end NonUnital
 
@@ -1293,20 +1289,20 @@ instance : IntCast (α →ᵇ R) :=
 theorem coe_intCast (n : ℤ) : ((n : α →ᵇ R) : α → R) = n := rfl
 #align bounded_continuous_function.coe_int_cast BoundedContinuousFunction.coe_intCast
 
-instance ring : Ring (α →ᵇ R) :=
+instance instRing : Ring (α →ᵇ R) :=
   DFunLike.coe_injective.ring _ coe_zero coe_one coe_add coe_mul coe_neg coe_sub
     (fun _ _ => coe_nsmul _ _) (fun _ _ => coe_zsmul _ _) (fun _ _ => coe_pow _ _) coe_natCast
     coe_intCast
 
-instance : SeminormedRing (α →ᵇ R) :=
-  { show Ring (α →ᵇ R) from inferInstance,  -- Porting note: this was not present in the original
-    BoundedContinuousFunction.nonUnitalSeminormedRing with }
+instance instSeminormedRing : SeminormedRing (α →ᵇ R) where
+  __ := instRing
+  __ := instNonUnitalSeminormedRing
 
 end Seminormed
 
-instance [NormedRing R] : NormedRing (α →ᵇ R) :=
-  { show Ring (α →ᵇ R) from inferInstance,  -- Porting note: this was not present in the original
-    BoundedContinuousFunction.nonUnitalNormedRing with }
+instance instNormedRing [NormedRing R] : NormedRing (α →ᵇ R) where
+  __ := instRing
+  __ := instNonUnitalNormedRing
 
 end NormedRing
 
@@ -1322,19 +1318,20 @@ pointwise operations and checking that they are compatible with the uniform dist
 
 variable [TopologicalSpace α] {R : Type*}
 
-instance commRing [SeminormedCommRing R] : CommRing (α →ᵇ R) :=
-  { BoundedContinuousFunction.ring with
-    mul_comm := fun _ _ => ext fun _ => mul_comm _ _ }
+instance instCommRing [SeminormedCommRing R] : CommRing (α →ᵇ R) where
+  mul_comm _ _ := ext fun _ ↦ mul_comm _ _
 
-instance [SeminormedCommRing R] : SeminormedCommRing (α →ᵇ R) :=
-  { BoundedContinuousFunction.commRing, BoundedContinuousFunction.seminormedAddCommGroup with
-    -- Porting note (#10888): added proof for `norm_mul`
-    norm_mul := norm_mul_le }
+instance instSeminormedCommRing [SeminormedCommRing R] : SeminormedCommRing (α →ᵇ R) where
+  __ := instCommRing
+  __ := instSeminormedAddCommGroup
+  -- Porting note (#10888): Added proof for `norm_mul`
+  norm_mul := norm_mul_le
 
-instance [NormedCommRing R] : NormedCommRing (α →ᵇ R) :=
-  { BoundedContinuousFunction.commRing, BoundedContinuousFunction.normedAddCommGroup with
-    -- Porting note (#10888): added proof for `norm_mul`
-    norm_mul := norm_mul_le }
+instance instNormedCommRing [NormedCommRing R] : NormedCommRing (α →ᵇ R) where
+  __ := instCommRing
+  __ := instNormedAddCommGroup
+  -- Porting note (#10888): Added proof for `norm_mul`
+  norm_mul := norm_mul_le
 
 end NormedCommRing
 
@@ -1363,14 +1360,11 @@ def C : 𝕜 →+* α →ᵇ γ where
 set_option linter.uppercaseLean3 false in
 #align bounded_continuous_function.C BoundedContinuousFunction.C
 
--- Porting note: named this instance, to use it in `instance : NormedAlgebra 𝕜 (α →ᵇ γ)`
-instance algebra : Algebra 𝕜 (α →ᵇ γ) :=
-  { BoundedContinuousFunction.module,
-    BoundedContinuousFunction.ring (α := α) (R := γ) with
-    toRingHom := C
-    commutes' := fun _ _ => ext fun _ => Algebra.commutes' _ _
-    smul_def' := fun _ _ => ext fun _ => Algebra.smul_def' _ _ }
-#align bounded_continuous_function.algebra BoundedContinuousFunction.algebra
+instance instAlgebra : Algebra 𝕜 (α →ᵇ γ) where
+  toRingHom := C
+  commutes' _ _ := ext fun _ ↦ Algebra.commutes' _ _
+  smul_def' _ _ := ext fun _ ↦ Algebra.smul_def' _ _
+#align bounded_continuous_function.algebra BoundedContinuousFunction.instAlgebra
 
 @[simp]
 theorem algebraMap_apply (k : 𝕜) (a : α) : algebraMap 𝕜 (α →ᵇ γ) k a = k • (1 : γ) := by
@@ -1378,10 +1372,9 @@ theorem algebraMap_apply (k : 𝕜) (a : α) : algebraMap 𝕜 (α →ᵇ γ) k
   rfl
 #align bounded_continuous_function.algebra_map_apply BoundedContinuousFunction.algebraMap_apply
 
--- Porting note: `show Algebra` was not present in the original
-instance : NormedAlgebra 𝕜 (α →ᵇ γ) :=
-  { show Algebra 𝕜 (α →ᵇ γ) from inferInstance,
-    BoundedContinuousFunction.normedSpace with }
+instance instNormedAlgebra : NormedAlgebra 𝕜 (α →ᵇ γ) where
+  __ := instAlgebra
+  __ := instNormedSpace
 
 /-!
 ### Structure as normed module over scalar functions
@@ -1391,22 +1384,22 @@ functions from `α` to `β` is naturally a module over the algebra of bounded co
 functions from `α` to `𝕜`. -/
 
 
-instance hasSMul' : SMul (α →ᵇ 𝕜) (α →ᵇ β) where
+instance instSMul' : SMul (α →ᵇ 𝕜) (α →ᵇ β) where
   smul f g :=
     ofNormedAddCommGroup (fun x => f x • g x) (f.continuous.smul g.continuous) (‖f‖ * ‖g‖) fun x =>
       calc
         ‖f x • g x‖ ≤ ‖f x‖ * ‖g x‖ := norm_smul_le _ _
         _ ≤ ‖f‖ * ‖g‖ :=
           mul_le_mul (f.norm_coe_le_norm _) (g.norm_coe_le_norm _) (norm_nonneg _) (norm_nonneg _)
-#align bounded_continuous_function.has_smul' BoundedContinuousFunction.hasSMul'
+#align bounded_continuous_function.has_smul' BoundedContinuousFunction.instSMul'
 
-instance module' : Module (α →ᵇ 𝕜) (α →ᵇ β) :=
+instance instModule' : Module (α →ᵇ 𝕜) (α →ᵇ β) :=
   Module.ofMinimalAxioms
       (fun _ _ _ => ext fun _ => smul_add _ _ _)
       (fun _ _ _ => ext fun _ => add_smul _ _ _)
       (fun _ _ _ => ext fun _ => mul_smul _ _ _)
       (fun f => ext fun x => one_smul 𝕜 (f x))
-#align bounded_continuous_function.module' BoundedContinuousFunction.module'
+#align bounded_continuous_function.module' BoundedContinuousFunction.instModule'
 
 /- TODO: When `NormedModule` has been added to `Analysis.NormedSpace.Basic`, this
 shows that the space of bounded continuous functions from `α` to `β` is naturally a normed
@@ -1450,7 +1443,7 @@ variable {𝕜 : Type*} [NormedField 𝕜] [StarRing 𝕜] [TopologicalSpace α]
 
 variable [NormedSpace 𝕜 β] [StarModule 𝕜 β]
 
-instance starAddMonoid : StarAddMonoid (α →ᵇ β) where
+instance instStarAddMonoid : StarAddMonoid (α →ᵇ β) where
   star f := f.comp star starNormedAddGroupHom.lipschitz
   star_involutive f := ext fun x => star_star (f x)
   star_add f g := ext fun x => star_add (f x) (g x)
@@ -1465,10 +1458,10 @@ theorem coe_star (f : α →ᵇ β) : ⇑(star f) = star (⇑f) := rfl
 theorem star_apply (f : α →ᵇ β) (x : α) : star f x = star (f x) := rfl
 #align bounded_continuous_function.star_apply BoundedContinuousFunction.star_apply
 
-instance : NormedStarGroup (α →ᵇ β) where
+instance instNormedStarGroup : NormedStarGroup (α →ᵇ β) where
   norm_star f := by simp only [norm_eq, star_apply, norm_star]
 
-instance : StarModule 𝕜 (α →ᵇ β) where
+instance instStarModule : StarModule 𝕜 (α →ᵇ β) where
   star_smul k f := ext fun x => star_smul k (f x)
 
 end NormedAddCommGroup
@@ -1478,15 +1471,14 @@ section CstarRing
 variable [TopologicalSpace α]
 variable [NonUnitalNormedRing β] [StarRing β]
 
-instance [NormedStarGroup β] : StarRing (α →ᵇ β) :=
-  { BoundedContinuousFunction.starAddMonoid with
-    star_mul := fun f g => ext fun x => star_mul (f x) (g x) }
+instance instStarRing [NormedStarGroup β] : StarRing (α →ᵇ β) where
+  __ := instStarAddMonoid
+  star_mul f g := ext fun x ↦ star_mul (f x) (g x)
 
 variable [CstarRing β]
 
-instance : CstarRing (α →ᵇ β) where
-  norm_star_mul_self := by
-    intro f
+instance instCstarRing : CstarRing (α →ᵇ β) where
+  norm_star_mul_self {f} := by
     refine' le_antisymm _ _
     · rw [← sq, norm_le (sq_nonneg _)]
       dsimp [star_apply]
@@ -1506,58 +1498,56 @@ section NormedLatticeOrderedGroup
 
 variable [TopologicalSpace α] [NormedLatticeAddCommGroup β]
 
-instance partialOrder : PartialOrder (α →ᵇ β) :=
+instance instPartialOrder : PartialOrder (α →ᵇ β) :=
   PartialOrder.lift (fun f => f.toFun) (by simp [Injective])
 
-/-- Continuous normed lattice group valued functions form a meet-semilattice. -/
-instance semilatticeInf : SemilatticeInf (α →ᵇ β) :=
-  { BoundedContinuousFunction.partialOrder with
-    inf := fun f g =>
-      { toFun := fun t => f t ⊓ g t
-        continuous_toFun := f.continuous.inf g.continuous
-        map_bounded' := by
-          obtain ⟨C₁, hf⟩ := f.bounded
-          obtain ⟨C₂, hg⟩ := g.bounded
-          refine' ⟨C₁ + C₂, fun x y => _⟩
-          simp_rw [NormedAddCommGroup.dist_eq] at hf hg ⊢
-          exact (norm_inf_sub_inf_le_add_norm _ _ _ _).trans (add_le_add (hf _ _) (hg _ _)) }
-    inf_le_left := fun f g => ContinuousMap.le_def.mpr fun _ => inf_le_left
-    inf_le_right := fun f g => ContinuousMap.le_def.mpr fun _ => inf_le_right
-    le_inf := fun f g₁ g₂ w₁ w₂ =>
-      ContinuousMap.le_def.mpr fun _ =>
-        le_inf (ContinuousMap.le_def.mp w₁ _) (ContinuousMap.le_def.mp w₂ _) }
-
-instance semilatticeSup : SemilatticeSup (α →ᵇ β) :=
-  { BoundedContinuousFunction.partialOrder with
-    sup := fun f g =>
-      { toFun := fun t => f t ⊔ g t
-        continuous_toFun := f.continuous.sup g.continuous
-        map_bounded' := by
-          obtain ⟨C₁, hf⟩ := f.bounded
-          obtain ⟨C₂, hg⟩ := g.bounded
-          refine' ⟨C₁ + C₂, fun x y => _⟩
-          simp_rw [NormedAddCommGroup.dist_eq] at hf hg ⊢
-          exact (norm_sup_sub_sup_le_add_norm _ _ _ _).trans (add_le_add (hf _ _) (hg _ _)) }
-    le_sup_left := fun f g => ContinuousMap.le_def.mpr fun _ => le_sup_left
-    le_sup_right := fun f g => ContinuousMap.le_def.mpr fun _ => le_sup_right
-    sup_le := fun f g₁ g₂ w₁ w₂ =>
-      ContinuousMap.le_def.mpr fun _ =>
-        sup_le (ContinuousMap.le_def.mp w₁ _) (ContinuousMap.le_def.mp w₂ _) }
-
-instance lattice : Lattice (α →ᵇ β) :=
-  { BoundedContinuousFunction.semilatticeSup, BoundedContinuousFunction.semilatticeInf with }
-
-@[simp]
-theorem coeFn_sup (f g : α →ᵇ β) : ⇑(f ⊔ g) = ⇑f ⊔ ⇑g := rfl
-#align bounded_continuous_function.coe_fn_sup BoundedContinuousFunction.coeFn_sup
-
-@[simp]
-theorem coeFn_abs (f : α →ᵇ β) : ⇑|f| = |⇑f| := rfl
-#align bounded_continuous_function.coe_fn_abs BoundedContinuousFunction.coeFn_abs
-
-instance : NormedLatticeAddCommGroup (α →ᵇ β) :=
-  { BoundedContinuousFunction.lattice,
-    BoundedContinuousFunction.seminormedAddCommGroup with
+instance instSup : Sup (α →ᵇ β) where
+  sup f g :=
+    { toFun := f ⊔ g
+      continuous_toFun := f.continuous.sup g.continuous
+      map_bounded' := by
+        obtain ⟨C₁, hf⟩ := f.bounded
+        obtain ⟨C₂, hg⟩ := g.bounded
+        refine ⟨C₁ + C₂, fun x y ↦ ?_⟩
+        simp_rw [NormedAddCommGroup.dist_eq] at hf hg ⊢
+        exact (norm_sup_sub_sup_le_add_norm _ _ _ _).trans (add_le_add (hf _ _) (hg _ _)) }
+
+instance instInf : Inf (α →ᵇ β) where
+  inf f g :=
+    { toFun := f ⊓ g
+      continuous_toFun := f.continuous.inf g.continuous
+      map_bounded' := by
+        obtain ⟨C₁, hf⟩ := f.bounded
+        obtain ⟨C₂, hg⟩ := g.bounded
+        refine ⟨C₁ + C₂, fun x y ↦ ?_⟩
+        simp_rw [NormedAddCommGroup.dist_eq] at hf hg ⊢
+        exact (norm_inf_sub_inf_le_add_norm _ _ _ _).trans (add_le_add (hf _ _) (hg _ _)) }
+
+@[simp, norm_cast] lemma coe_sup (f g : α →ᵇ β) : ⇑(f ⊔ g) = ⇑f ⊔ ⇑g := rfl
+#align bounded_continuous_function.coe_fn_sup BoundedContinuousFunction.coe_sup
+
+@[simp, norm_cast] lemma coe_inf (f g : α →ᵇ β) : ⇑(f ⊓ g) = ⇑f ⊓ ⇑g := rfl
+
+instance instSemilatticeSup : SemilatticeSup (α →ᵇ β) :=
+  DFunLike.coe_injective.semilatticeSup _ coe_sup
+
+instance instSemilatticeInf : SemilatticeInf (α →ᵇ β) :=
+  DFunLike.coe_injective.semilatticeInf _ coe_inf
+
+instance instLattice : Lattice (α →ᵇ β) := DFunLike.coe_injective.lattice _ coe_sup coe_inf
+
+@[simp, norm_cast] lemma coe_abs (f : α →ᵇ β) : ⇑|f| = |⇑f| := rfl
+#align bounded_continuous_function.coe_fn_abs BoundedContinuousFunction.coe_abs
+
+@[simp, norm_cast] lemma coe_posPart (f : α →ᵇ β) : ⇑f⁺ = (⇑f)⁺ := rfl
+@[simp, norm_cast] lemma coe_negPart (f : α →ᵇ β) : ⇑f⁻ = (⇑f)⁻ := rfl
+
+-- 2024-02-21
+@[deprecated] alias coeFn_sup := coe_sup
+@[deprecated] alias coeFn_abs := coe_abs
+
+instance instNormedLatticeAddCommGroup : NormedLatticeAddCommGroup (α →ᵇ β) :=
+  { instSeminormedAddCommGroup with
     add_le_add_left := by
       intro f g h₁ h t
       simp only [coe_to_continuous_fun, Pi.add_apply, add_le_add_iff_left, coe_add,
@@ -1598,6 +1588,7 @@ def nnnorm (f : α →ᵇ ℝ) : α →ᵇ ℝ≥0 :=
 theorem nnnorm_coeFn_eq (f : α →ᵇ ℝ) : ⇑f.nnnorm = NNNorm.nnnorm ∘ ⇑f := rfl
 #align bounded_continuous_function.nnnorm_coe_fun_eq BoundedContinuousFunction.nnnorm_coeFn_eq
 
+-- TODO: Use `posPart` and `negPart` here
 /-- Decompose a bounded continuous function to its positive and negative parts. -/
 theorem self_eq_nnrealPart_sub_nnrealPart_neg (f : α →ᵇ ℝ) :
     ⇑f = (↑) ∘ f.nnrealPart - (↑) ∘ (-f).nnrealPart := by
@@ -1621,6 +1612,7 @@ section
 
 variable {α : Type*} [TopologicalSpace α]
 
+-- TODO: `f + const _ ‖f‖` is just `f⁺`
 lemma add_norm_nonneg (f : α →ᵇ ℝ) :
     0 ≤ f + const _ ‖f‖ := by
   intro x

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -67,7 +67,6 @@ namespace BoundedContinuousFunction
 section Basics
 
 variable [TopologicalSpace α] [PseudoMetricSpace β] [PseudoMetricSpace γ]
-
 variable {f g : α →ᵇ β} {x : α} {C : ℝ}
 
 instance : FunLike (α →ᵇ β) α β where
@@ -510,7 +509,6 @@ end Basics
 section ArzelaAscoli
 
 variable [TopologicalSpace α] [CompactSpace α] [PseudoMetricSpace β]
-
 variable {f g : α →ᵇ β} {x : α} {C : ℝ}
 
 /- Arzela-Ascoli theorem asserts that, on a compact space, a set of functions sharing
@@ -659,9 +657,7 @@ names (for example, `coe_mul`) to conflict with later lemma names for normed rin
 trivial inconvenience, but in any case there are no obvious applications of the multiplicative
 version. -/
 variable [TopologicalSpace α] [PseudoMetricSpace β] [AddMonoid β]
-
 variable [LipschitzAdd β]
-
 variable (f g : α →ᵇ β) {x : α} {C : ℝ}
 
 /-- The pointwise sum of two bounded continuous functions is again bounded continuous. -/
@@ -781,7 +777,6 @@ section NormedAddCommGroup
 continuous functions from `α` to `β` inherits a normed group structure, by using
 pointwise operations and checking that they are compatible with the uniform distance. -/
 variable [TopologicalSpace α] [SeminormedAddCommGroup β]
-
 variable (f g : α →ᵇ β) {x : α} {C : ℝ}
 
 instance : Norm (α →ᵇ β) :=
@@ -1114,7 +1109,6 @@ end MulAction
 section DistribMulAction
 
 variable [MonoidWithZero 𝕜] [AddMonoid β] [DistribMulAction 𝕜 β] [BoundedSMul 𝕜 β]
-
 variable [LipschitzAdd β]
 
 instance : DistribMulAction 𝕜 (α →ᵇ β) :=
@@ -1125,9 +1119,7 @@ end DistribMulAction
 section Module
 
 variable [Semiring 𝕜] [AddCommMonoid β] [Module 𝕜 β] [BoundedSMul 𝕜 β]
-
 variable {f g : α →ᵇ β} {x : α} {C : ℝ}
-
 variable [LipschitzAdd β]
 
 instance module : Module 𝕜 (α →ᵇ β) :=
@@ -1171,9 +1163,7 @@ pointwise operations and checking that they are compatible with the uniform dist
 
 
 variable {𝕜 : Type*}
-
 variable [TopologicalSpace α] [SeminormedAddCommGroup β]
-
 variable {f g : α →ᵇ β} {x : α} {C : ℝ}
 
 instance normedSpace [NormedField 𝕜] [NormedSpace 𝕜 β] : NormedSpace 𝕜 (α →ᵇ β) :=
@@ -1183,9 +1173,7 @@ instance normedSpace [NormedField 𝕜] [NormedSpace 𝕜 β] : NormedSpace 𝕜
       norm_smul c (f x) ▸ mul_le_mul_of_nonneg_left (f.norm_coe_le_norm _) (norm_nonneg _)⟩
 
 variable [NontriviallyNormedField 𝕜] [NormedSpace 𝕜 β]
-
 variable [SeminormedAddCommGroup γ] [NormedSpace 𝕜 γ]
-
 variable (α)
 
 -- TODO does this work in the `BoundedSMul` setting, too?
@@ -1361,11 +1349,8 @@ pointwise operations and checking that they are compatible with the uniform dist
 
 
 variable {𝕜 : Type*} [NormedField 𝕜]
-
 variable [TopologicalSpace α] [SeminormedAddCommGroup β] [NormedSpace 𝕜 β]
-
 variable [NormedRing γ] [NormedAlgebra 𝕜 γ]
-
 variable {f g : α →ᵇ γ} {x : α} {c : 𝕜}
 
 /-- `BoundedContinuousFunction.const` as a `RingHom`. -/
@@ -1491,7 +1476,6 @@ end NormedAddCommGroup
 section CstarRing
 
 variable [TopologicalSpace α]
-
 variable [NonUnitalNormedRing β] [StarRing β]
 
 instance [NormedStarGroup β] : StarRing (α →ᵇ β) :=

ball for "bounded forall" and bex for "bounded exists" are from experience very confusing abbreviations. This PR renames them to forall_mem and exists_mem in the few Set lemma names that mention them.

Also deprecate ball_image_of_ball, mem_image_elim, mem_image_elim_on since those lemmas are duplicates of the renamed lemmas (apart from argument order and implicitness, which I am also fixing by making the binder in the RHS of forall_mem_image semi-implicit), have obscure names and are completely unused.

@@ -248,7 +248,7 @@ theorem dist_zero_of_empty [IsEmpty α] : dist f g = 0 := by
 theorem dist_eq_iSup : dist f g = ⨆ x : α, dist (f x) (g x) := by
   cases isEmpty_or_nonempty α; · rw [iSup_of_empty', Real.sSup_empty, dist_zero_of_empty]
   refine' (dist_le_iff_of_nonempty.mpr <| le_ciSup _).antisymm (ciSup_le dist_coe_le_dist)
-  exact dist_set_exists.imp fun C hC => forall_range_iff.2 hC.2
+  exact dist_set_exists.imp fun C hC => forall_mem_range.2 hC.2
 #align bounded_continuous_function.dist_eq_supr BoundedContinuousFunction.dist_eq_iSup
 
 theorem nndist_eq_iSup : nndist f g = ⨆ x : α, nndist (f x) (g x) :=

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

@@ -23,7 +23,8 @@ the uniform distance.
 
 noncomputable section
 
-open Topology Bornology Classical NNReal uniformity UniformConvergence
+open scoped Classical
+open Topology Bornology NNReal uniformity UniformConvergence
 
 open Set Filter Metric Function
 

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -357,7 +357,7 @@ instance [CompleteSpace β] : CompleteSpace (α →ᵇ β) :=
         dist (F x) (F y) ≤ dist (f 0 x) (f 0 y) + (dist (f 0 x) (F x) + dist (f 0 y) (F y)) :=
           dist_triangle4_left _ _ _ _
         _ ≤ C + (b 0 + b 0) := add_le_add (hC _ _) (add_le_add (fF_bdd _ _) (fF_bdd _ _))
-                               -- porting note: was --by mono*
+                               -- Porting note: was --by mono*
     · -- Check that `F` is close to `f N` in distance terms
       refine' tendsto_iff_dist_tendsto_zero.2 (squeeze_zero (fun _ => dist_nonneg) _ b_lim)
       exact fun N => (dist_le (b0 _)).2 fun x => fF_bdd x N
@@ -1310,13 +1310,13 @@ instance ring : Ring (α →ᵇ R) :=
     coe_intCast
 
 instance : SeminormedRing (α →ᵇ R) :=
-  { show Ring (α →ᵇ R) from inferInstance,  -- porting note: this was not present in the original
+  { show Ring (α →ᵇ R) from inferInstance,  -- Porting note: this was not present in the original
     BoundedContinuousFunction.nonUnitalSeminormedRing with }
 
 end Seminormed
 
 instance [NormedRing R] : NormedRing (α →ᵇ R) :=
-  { show Ring (α →ᵇ R) from inferInstance,  -- porting note: this was not present in the original
+  { show Ring (α →ᵇ R) from inferInstance,  -- Porting note: this was not present in the original
     BoundedContinuousFunction.nonUnitalNormedRing with }
 
 end NormedRing
@@ -1377,7 +1377,7 @@ def C : 𝕜 →+* α →ᵇ γ where
 set_option linter.uppercaseLean3 false in
 #align bounded_continuous_function.C BoundedContinuousFunction.C
 
--- porting note: named this instance, to use it in `instance : NormedAlgebra 𝕜 (α →ᵇ γ)`
+-- Porting note: named this instance, to use it in `instance : NormedAlgebra 𝕜 (α →ᵇ γ)`
 instance algebra : Algebra 𝕜 (α →ᵇ γ) :=
   { BoundedContinuousFunction.module,
     BoundedContinuousFunction.ring (α := α) (R := γ) with
@@ -1392,7 +1392,7 @@ theorem algebraMap_apply (k : 𝕜) (a : α) : algebraMap 𝕜 (α →ᵇ γ) k
   rfl
 #align bounded_continuous_function.algebra_map_apply BoundedContinuousFunction.algebraMap_apply
 
--- porting note: `show Algebra` was not present in the original
+-- Porting note: `show Algebra` was not present in the original
 instance : NormedAlgebra 𝕜 (α →ᵇ γ) :=
   { show Algebra 𝕜 (α →ᵇ γ) from inferInstance,
     BoundedContinuousFunction.normedSpace with }

Split the 2300-line behemoth OperatorNorm.lean into 8 smaller files, of which the largest is 600 lines.

@@ -3,13 +3,12 @@ Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Mario Carneiro, Yury Kudryashov, Heather Macbeth
 -/
+import Mathlib.Algebra.Module.MinimalAxioms
+import Mathlib.Topology.ContinuousFunction.Algebra
 import Mathlib.Analysis.Normed.Order.Lattice
-import Mathlib.Analysis.NormedSpace.OperatorNorm
+import Mathlib.Analysis.NormedSpace.OperatorNorm.Basic
 import Mathlib.Analysis.NormedSpace.Star.Basic
-import Mathlib.Data.Real.Sqrt
-import Mathlib.Topology.ContinuousFunction.Algebra
-import Mathlib.Topology.MetricSpace.Equicontinuity
-import Mathlib.Algebra.Module.MinimalAxioms
+import Mathlib.Analysis.NormedSpace.ContinuousLinearMap
 
 #align_import topology.continuous_function.bounded from "leanprover-community/mathlib"@"5dc275ec639221ca4d5f56938eb966f6ad9bc89f"
 

I loogled for every occurrence of "cast", Nat and "natCast" and where the casted nat was n, and made sure there were corresponding @[simp] lemmas for 0, 1, and OfNat.ofNat n. This is necessary in general for simp confluence. Example:

import Mathlib

variable {α : Type*} [LinearOrderedRing α] (m n : ℕ) [m.AtLeastTwo] [n.AtLeastTwo]

example : ((OfNat.ofNat m : ℕ) : α) ≤ ((OfNat.ofNat n : ℕ) : α) ↔ (OfNat.ofNat m : ℕ) ≤ (OfNat.ofNat n : ℕ) := by
  simp only [Nat.cast_le] -- this `@[simp]` lemma can apply

example : ((OfNat.ofNat m : ℕ) : α) ≤ ((OfNat.ofNat n : ℕ) : α) ↔ (OfNat.ofNat m : α) ≤ (OfNat.ofNat n : α) := by
  simp only [Nat.cast_ofNat] -- and so can this one

example : (OfNat.ofNat m : α) ≤ (OfNat.ofNat n : α) ↔ (OfNat.ofNat m : ℕ) ≤ (OfNat.ofNat n : ℕ) := by
  simp -- fails! `simp` doesn't have a lemma to bridge their results. confluence issue.

As far as I know, the only file this PR leaves with ofNat gaps is PartENat.lean. #8002 is addressing that file in parallel.

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -1292,6 +1292,12 @@ instance : NatCast (α →ᵇ R) :=
 theorem coe_natCast (n : ℕ) : ((n : α →ᵇ R) : α → R) = n := rfl
 #align bounded_continuous_function.coe_nat_cast BoundedContinuousFunction.coe_natCast
 
+-- See note [no_index around OfNat.ofNat]
+@[simp, norm_cast]
+theorem coe_ofNat (n : ℕ) [n.AtLeastTwo] :
+    ((no_index OfNat.ofNat n : α →ᵇ R) : α → R) = OfNat.ofNat n :=
+  rfl
+
 instance : IntCast (α →ᵇ R) :=
   ⟨fun n => BoundedContinuousFunction.const _ n⟩
 

Classifies by adding issue number (#10888) to porting notes claiming added proof.

@@ -217,7 +217,7 @@ instance : PseudoMetricSpace (α →ᵇ β) where
   dist_comm f g := by simp [dist_eq, dist_comm]
   dist_triangle f g h := (dist_le (add_nonneg dist_nonneg' dist_nonneg')).2
     fun x => le_trans (dist_triangle _ _ _) (add_le_add (dist_coe_le_dist _) (dist_coe_le_dist _))
-  -- Porting note: Added proof for `edist_dist`
+  -- Porting note (#10888): added proof for `edist_dist`
   edist_dist x y := by dsimp; congr; simp [dist_nonneg']
 
 /-- The type of bounded continuous functions, with the uniform distance, is a metric space. -/
@@ -999,7 +999,7 @@ instance seminormedAddCommGroup : SeminormedAddCommGroup (α →ᵇ β) where
 instance normedAddCommGroup {α β} [TopologicalSpace α] [NormedAddCommGroup β] :
     NormedAddCommGroup (α →ᵇ β) :=
   { BoundedContinuousFunction.seminormedAddCommGroup with
-    -- Porting note: Added a proof for `eq_of_dist_eq_zero`
+    -- Porting note (#10888): added proof for `eq_of_dist_eq_zero`
     eq_of_dist_eq_zero }
 
 theorem nnnorm_def : ‖f‖₊ = nndist f 0 := rfl
@@ -1334,12 +1334,12 @@ instance commRing [SeminormedCommRing R] : CommRing (α →ᵇ R) :=
 
 instance [SeminormedCommRing R] : SeminormedCommRing (α →ᵇ R) :=
   { BoundedContinuousFunction.commRing, BoundedContinuousFunction.seminormedAddCommGroup with
-    -- Porting note: Added proof for `norm_mul`
+    -- Porting note (#10888): added proof for `norm_mul`
     norm_mul := norm_mul_le }
 
 instance [NormedCommRing R] : NormedCommRing (α →ᵇ R) :=
   { BoundedContinuousFunction.commRing, BoundedContinuousFunction.normedAddCommGroup with
-    -- Porting note: Added proof for `norm_mul`
+    -- Porting note (#10888): added proof for `norm_mul`
     norm_mul := norm_mul_le }
 
 end NormedCommRing
@@ -1578,7 +1578,7 @@ instance : NormedLatticeAddCommGroup (α →ᵇ β) :=
       have i1 : ∀ t, ‖f t‖ ≤ ‖g t‖ := fun t => HasSolidNorm.solid (h t)
       rw [norm_le (norm_nonneg _)]
       exact fun t => (i1 t).trans (norm_coe_le_norm g t)
-    -- Porting note: Added a proof for `eq_of_dist_eq_zero`
+    -- Porting note (#10888): added proof for `eq_of_dist_eq_zero`
     eq_of_dist_eq_zero }
 
 end NormedLatticeOrderedGroup

@@ -544,9 +544,11 @@ theorem arzela_ascoli₁ [CompactSpace β] (A : Set (α →ᵇ β)) (closed : Is
     We extract finitely many of these sets that cover the whole space, by compactness. -/
   rcases isCompact_univ.elim_finite_subcover_image (fun x _ => (hU x).2.1) fun x _ =>
       mem_biUnion (mem_univ _) (hU x).1 with
-    ⟨tα, _, ⟨_⟩, htα⟩
+    ⟨tα, _, hfin, htα⟩
+  rcases hfin.nonempty_fintype with ⟨_⟩
   -- `tα: Set α`, `htα : univ ⊆ ⋃x ∈ tα, U x`
-  rcases @finite_cover_balls_of_compact β _ _ isCompact_univ _ ε₂0 with ⟨tβ, _, ⟨_⟩, htβ⟩
+  rcases @finite_cover_balls_of_compact β _ _ isCompact_univ _ ε₂0 with ⟨tβ, _, hfin, htβ⟩
+  rcases hfin.nonempty_fintype with ⟨_⟩
   -- `tβ : Set β`, `htβ : univ ⊆ ⋃y ∈ tβ, ball y ε₂`
   -- Associate to every point `y` in the space a nearby point `F y` in `tβ`
   choose F hF using fun y => show ∃ z ∈ tβ, dist y z < ε₂ by simpa using htβ (mem_univ y)

The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike is EquivLike, since that has a custom coe_injective' field that is easier to implement. All other classes should take FunLike or EquivLike as a parameter.

Zulip thread

Important changes

Previously, morphism classes would be Type-valued and extend FunLike:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

After this PR, they should be Prop-valued and take FunLike as a parameter:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  [FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

(Note that A B stay marked as outParam even though they are not purely required to be so due to the FunLike parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam is slightly faster.)

Similarly, MyEquivClass should take EquivLike as a parameter.

As a result, every mention of [MyHomClass F A B] should become [FunLike F A B] [MyHomClass F A B].

Remaining issues

Slower (failing) search

While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul is more expensive. This is due to suboptimal processing of arguments. For example:

variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)

theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y

example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _

Before this PR, applying map_mul f gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Since M and N are out_params, [MulHomClass F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found.

After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Now [FunLike F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found, before trying MulHomClass F M N which fails. Since the Mul hierarchy is very big, this can be slow to fail, especially when there is no such Mul instance.

A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N] because MulHomClass fails or succeeds much faster than the others.

As a consequence, the simpNF linter is much slower since by design it tries and fails to apply many map_ lemmas. The same issue occurs a few times in existing calls to simp [map_mul], where map_mul is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.

simp not firing sometimes

This affects map_smulₛₗ and related definitions. For simp lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw can find every argument to map_smulₛₗ successfully but simp can't: leanprover/lean4#3701.

Missing instances due to unification failing

Especially in the category theory library, we might sometimes have a type A which is also accessible as a synonym (Bundled A hA).1. Instance synthesis doesn't always work if we have f : A →* B but x * y : (Bundled A hA).1 or vice versa. This seems to be mostly fixed by keeping A B as outParams in MulHomClass F A B. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1 instead of using the syntax in the discrimination tree.)

Workaround for issues

The timeouts can be worked around for now by specifying which map_mul we mean, either as map_mul f for some explicit f, or as e.g. MonoidHomClass.map_mul.

map_smulₛₗ not firing as simp lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ a simp lemma instead of the generic map_smulₛₗ. Writing simp [map_smulₛₗ _] also works.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -54,7 +54,7 @@ section
 
 You should also extend this typeclass when you extend `BoundedContinuousFunction`. -/
 class BoundedContinuousMapClass (F : Type*) (α β : outParam <| Type*) [TopologicalSpace α]
-    [PseudoMetricSpace β] extends ContinuousMapClass F α β where
+    [PseudoMetricSpace β] [FunLike F α β] extends ContinuousMapClass F α β : Prop where
   map_bounded (f : F) : ∃ C, ∀ x y, dist (f x) (f y) ≤ C
 #align bounded_continuous_map_class BoundedContinuousMapClass
 
@@ -70,21 +70,18 @@ variable [TopologicalSpace α] [PseudoMetricSpace β] [PseudoMetricSpace γ]
 
 variable {f g : α →ᵇ β} {x : α} {C : ℝ}
 
-instance : BoundedContinuousMapClass (α →ᵇ β) α β where
+instance : FunLike (α →ᵇ β) α β where
   coe f := f.toFun
   coe_injective' f g h := by
     obtain ⟨⟨_, _⟩, _⟩ := f
     obtain ⟨⟨_, _⟩, _⟩ := g
     congr
+
+instance : BoundedContinuousMapClass (α →ᵇ β) α β where
   map_continuous f := f.continuous_toFun
   map_bounded f := f.map_bounded'
 
-/-- Helper instance for when there's too many metavariables to apply `DFunLike.hasCoeToFun`
-directly. -/
-instance : CoeFun (α →ᵇ β) fun _ => α → β :=
-  DFunLike.hasCoeToFun
-
-instance [BoundedContinuousMapClass F α β] : CoeTC F (α →ᵇ β) :=
+instance [FunLike F α β] [BoundedContinuousMapClass F α β] : CoeTC F (α →ᵇ β) :=
   ⟨fun f =>
     { toFun := f
       continuous_toFun := map_continuous f

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

@@ -1198,11 +1198,11 @@ protected def _root_.ContinuousLinearMap.compLeftContinuousBounded (g : β →L[
   LinearMap.mkContinuous
     { toFun := fun f =>
         ofNormedAddCommGroup (g ∘ f) (g.continuous.comp f.continuous) (‖g‖ * ‖f‖) fun x =>
-          g.le_op_norm_of_le (f.norm_coe_le_norm x)
+          g.le_opNorm_of_le (f.norm_coe_le_norm x)
       map_add' := fun f g => by ext; simp
       map_smul' := fun c f => by ext; simp } ‖g‖ fun f =>
         norm_ofNormedAddCommGroup_le _ (mul_nonneg (norm_nonneg g) (norm_nonneg f))
-          (fun x => by exact g.le_op_norm_of_le (f.norm_coe_le_norm x))
+          (fun x => by exact g.le_opNorm_of_le (f.norm_coe_le_norm x))
 #align continuous_linear_map.comp_left_continuous_bounded ContinuousLinearMap.compLeftContinuousBounded
 
 @[simp]

Rename

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

and related theorems.

@@ -1137,15 +1137,15 @@ instance module : Module 𝕜 (α →ᵇ β) :=
 variable (𝕜)
 
 /-- The evaluation at a point, as a continuous linear map from `α →ᵇ β` to `β`. -/
-def evalClm (x : α) : (α →ᵇ β) →L[𝕜] β where
+def evalCLM (x : α) : (α →ᵇ β) →L[𝕜] β where
   toFun f := f x
   map_add' f g := add_apply _ _
   map_smul' c f := smul_apply _ _ _
-#align bounded_continuous_function.eval_clm BoundedContinuousFunction.evalClm
+#align bounded_continuous_function.eval_clm BoundedContinuousFunction.evalCLM
 
 @[simp]
-theorem evalClm_apply (x : α) (f : α →ᵇ β) : evalClm 𝕜 x f = f x := rfl
-#align bounded_continuous_function.eval_clm_apply BoundedContinuousFunction.evalClm_apply
+theorem evalCLM_apply (x : α) (f : α →ᵇ β) : evalCLM 𝕜 x f = f x := rfl
+#align bounded_continuous_function.eval_clm_apply BoundedContinuousFunction.evalCLM_apply
 
 variable (α β)
 

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -79,10 +79,10 @@ instance : BoundedContinuousMapClass (α →ᵇ β) α β where
   map_continuous f := f.continuous_toFun
   map_bounded f := f.map_bounded'
 
-/-- Helper instance for when there's too many metavariables to apply `FunLike.hasCoeToFun`
+/-- Helper instance for when there's too many metavariables to apply `DFunLike.hasCoeToFun`
 directly. -/
 instance : CoeFun (α →ᵇ β) fun _ => α → β :=
-  FunLike.hasCoeToFun
+  DFunLike.hasCoeToFun
 
 instance [BoundedContinuousMapClass F α β] : CoeTC F (α →ᵇ β) :=
   ⟨fun f =>
@@ -111,7 +111,7 @@ protected theorem continuous (f : α →ᵇ β) : Continuous f :=
 
 @[ext]
 theorem ext (h : ∀ x, f x = g x) : f = g :=
-  FunLike.ext _ _ h
+  DFunLike.ext _ _ h
 #align bounded_continuous_function.ext BoundedContinuousFunction.ext
 
 theorem isBounded_range (f : α →ᵇ β) : IsBounded (range f) :=
@@ -475,7 +475,7 @@ nonrec theorem extend_apply' {f : α ↪ δ} {x : δ} (hx : x ∉ range f) (g :
 #align bounded_continuous_function.extend_apply' BoundedContinuousFunction.extend_apply'
 
 theorem extend_of_empty [IsEmpty α] (f : α ↪ δ) (g : α →ᵇ β) (h : δ →ᵇ β) : extend f g h = h :=
-  FunLike.coe_injective <| Function.extend_of_isEmpty f g h
+  DFunLike.coe_injective <| Function.extend_of_isEmpty f g h
 #align bounded_continuous_function.extend_of_empty BoundedContinuousFunction.extend_of_empty
 
 @[simp]
@@ -635,7 +635,7 @@ theorem mkOfCompact_one [CompactSpace α] : mkOfCompact (1 : C(α, β)) = 1 := r
 
 @[to_additive]
 theorem forall_coe_one_iff_one (f : α →ᵇ β) : (∀ x, f x = 1) ↔ f = 1 :=
-  (@FunLike.ext_iff _ _ _ _ f 1).symm
+  (@DFunLike.ext_iff _ _ _ _ f 1).symm
 #align bounded_continuous_function.forall_coe_one_iff_one BoundedContinuousFunction.forall_coe_one_iff_one
 #align bounded_continuous_function.forall_coe_zero_iff_zero BoundedContinuousFunction.forall_coe_zero_iff_zero
 
@@ -716,7 +716,7 @@ theorem nsmul_apply (r : ℕ) (f : α →ᵇ β) (v : α) : (r • f) v = r •
 #align bounded_continuous_function.nsmul_apply BoundedContinuousFunction.nsmul_apply
 
 instance addMonoid : AddMonoid (α →ᵇ β) :=
-  FunLike.coe_injective.addMonoid _ coe_zero coe_add fun _ _ => coe_nsmul _ _
+  DFunLike.coe_injective.addMonoid _ coe_zero coe_add fun _ _ => coe_nsmul _ _
 
 instance : LipschitzAdd (α →ᵇ β) where
   lipschitz_add :=
@@ -991,7 +991,7 @@ theorem zsmul_apply (r : ℤ) (f : α →ᵇ β) (v : α) : (r • f) v = r •
 #align bounded_continuous_function.zsmul_apply BoundedContinuousFunction.zsmul_apply
 
 instance : AddCommGroup (α →ᵇ β) :=
-  FunLike.coe_injective.addCommGroup _ coe_zero coe_add coe_neg coe_sub (fun _ _ => coe_nsmul _ _)
+  DFunLike.coe_injective.addCommGroup _ coe_zero coe_add coe_neg coe_sub (fun _ _ => coe_nsmul _ _)
     fun _ _ => coe_zsmul _ _
 
 instance seminormedAddCommGroup : SeminormedAddCommGroup (α →ᵇ β) where
@@ -1108,7 +1108,7 @@ section MulAction
 variable [MonoidWithZero 𝕜] [Zero β] [MulAction 𝕜 β] [BoundedSMul 𝕜 β]
 
 instance : MulAction 𝕜 (α →ᵇ β) :=
-  FunLike.coe_injective.mulAction _ coe_smul
+  DFunLike.coe_injective.mulAction _ coe_smul
 
 end MulAction
 
@@ -1119,7 +1119,7 @@ variable [MonoidWithZero 𝕜] [AddMonoid β] [DistribMulAction 𝕜 β] [Bounde
 variable [LipschitzAdd β]
 
 instance : DistribMulAction 𝕜 (α →ᵇ β) :=
-  Function.Injective.distribMulAction ⟨⟨_, coe_zero⟩, coe_add⟩ FunLike.coe_injective coe_smul
+  Function.Injective.distribMulAction ⟨⟨_, coe_zero⟩, coe_add⟩ DFunLike.coe_injective coe_smul
 
 end DistribMulAction
 
@@ -1132,7 +1132,7 @@ variable {f g : α →ᵇ β} {x : α} {C : ℝ}
 variable [LipschitzAdd β]
 
 instance module : Module 𝕜 (α →ᵇ β) :=
-  Function.Injective.module _ ⟨⟨_, coe_zero⟩, coe_add⟩ FunLike.coe_injective coe_smul
+  Function.Injective.module _ ⟨⟨_, coe_zero⟩, coe_add⟩ DFunLike.coe_injective coe_smul
 
 variable (𝕜)
 
@@ -1244,7 +1244,7 @@ theorem mul_apply (f g : α →ᵇ R) (x : α) : (f * g) x = f x * g x := rfl
 #align bounded_continuous_function.mul_apply BoundedContinuousFunction.mul_apply
 
 instance : NonUnitalRing (α →ᵇ R) :=
-  FunLike.coe_injective.nonUnitalRing _ coe_zero coe_add coe_mul coe_neg coe_sub
+  DFunLike.coe_injective.nonUnitalRing _ coe_zero coe_add coe_mul coe_neg coe_sub
     (fun _ _ => coe_nsmul _ _) fun _ _ => coe_zsmul _ _
 
 instance nonUnitalSeminormedRing : NonUnitalSeminormedRing (α →ᵇ R) :=
@@ -1301,7 +1301,7 @@ theorem coe_intCast (n : ℤ) : ((n : α →ᵇ R) : α → R) = n := rfl
 #align bounded_continuous_function.coe_int_cast BoundedContinuousFunction.coe_intCast
 
 instance ring : Ring (α →ᵇ R) :=
-  FunLike.coe_injective.ring _ coe_zero coe_one coe_add coe_mul coe_neg coe_sub
+  DFunLike.coe_injective.ring _ coe_zero coe_one coe_add coe_mul coe_neg coe_sub
     (fun _ _ => coe_nsmul _ _) (fun _ _ => coe_zsmul _ _) (fun _ _ => coe_pow _ _) coe_natCast
     coe_intCast
 

This changes the typeclass notation approach with plain functions.

Followup to #9553. Part of #9411

@@ -1591,7 +1591,7 @@ variable [TopologicalSpace α]
 /-- The nonnegative part of a bounded continuous `ℝ`-valued function as a bounded
 continuous `ℝ≥0`-valued function. -/
 def nnrealPart (f : α →ᵇ ℝ) : α →ᵇ ℝ≥0 :=
-  BoundedContinuousFunction.comp _ (show LipschitzWith 1 Real.toNNReal from lipschitzWith_pos) f
+  BoundedContinuousFunction.comp _ (show LipschitzWith 1 Real.toNNReal from lipschitzWith_posPart) f
 #align bounded_continuous_function.nnreal_part BoundedContinuousFunction.nnrealPart
 
 @[simp]

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

In some rare cases, golf proofs that needed fixing.

@@ -537,8 +537,7 @@ theorem arzela_ascoli₁ [CompactSpace β] (A : Set (α →ᵇ β)) (closed : Is
     continuity to extend the closeness on tα to closeness everywhere. -/
   have ε₂0 : ε₂ > 0 := half_pos (half_pos ε₁0)
   have : ∀ x : α, ∃ U, x ∈ U ∧ IsOpen U ∧
-      ∀ (y) (_ : y ∈ U) (z) (_ : z ∈ U) {f : α →ᵇ β}, f ∈ A → dist (f y) (f z) < ε₂ :=
-    fun x =>
+      ∀ y ∈ U, ∀ z ∈ U, ∀ {f : α →ᵇ β}, f ∈ A → dist (f y) (f z) < ε₂ := fun x =>
     let ⟨U, nhdsU, hU⟩ := H x _ ε₂0
     let ⟨V, VU, openV, xV⟩ := _root_.mem_nhds_iff.1 nhdsU
     ⟨V, xV, openV, fun y hy z hz f hf => hU y (VU hy) z (VU hz) ⟨f, hf⟩⟩

Normalising to naming convention rule number 6.

@@ -1402,14 +1402,14 @@ functions from `α` to `β` is naturally a module over the algebra of bounded co
 functions from `α` to `𝕜`. -/
 
 
-instance hasSmul' : SMul (α →ᵇ 𝕜) (α →ᵇ β) where
+instance hasSMul' : SMul (α →ᵇ 𝕜) (α →ᵇ β) where
   smul f g :=
     ofNormedAddCommGroup (fun x => f x • g x) (f.continuous.smul g.continuous) (‖f‖ * ‖g‖) fun x =>
       calc
         ‖f x • g x‖ ≤ ‖f x‖ * ‖g x‖ := norm_smul_le _ _
         _ ≤ ‖f‖ * ‖g‖ :=
           mul_le_mul (f.norm_coe_le_norm _) (g.norm_coe_le_norm _) (norm_nonneg _) (norm_nonneg _)
-#align bounded_continuous_function.has_smul' BoundedContinuousFunction.hasSmul'
+#align bounded_continuous_function.has_smul' BoundedContinuousFunction.hasSMul'
 
 instance module' : Module (α →ᵇ 𝕜) (α →ᵇ β) :=
   Module.ofMinimalAxioms

This makes it consistent with Ring, Field and Group.

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -9,6 +9,7 @@ import Mathlib.Analysis.NormedSpace.Star.Basic
 import Mathlib.Data.Real.Sqrt
 import Mathlib.Topology.ContinuousFunction.Algebra
 import Mathlib.Topology.MetricSpace.Equicontinuity
+import Mathlib.Algebra.Module.MinimalAxioms
 
 #align_import topology.continuous_function.bounded from "leanprover-community/mathlib"@"5dc275ec639221ca4d5f56938eb966f6ad9bc89f"
 
@@ -1411,11 +1412,11 @@ instance hasSmul' : SMul (α →ᵇ 𝕜) (α →ᵇ β) where
 #align bounded_continuous_function.has_smul' BoundedContinuousFunction.hasSmul'
 
 instance module' : Module (α →ᵇ 𝕜) (α →ᵇ β) :=
-  Module.ofCore <|
-    { smul_add := fun _ _ _ => ext fun _ => smul_add _ _ _
-      add_smul := fun _ _ _ => ext fun _ => add_smul _ _ _
-      mul_smul := fun _ _ _ => ext fun _ => mul_smul _ _ _
-      one_smul := fun f => ext fun x => one_smul 𝕜 (f x) }
+  Module.ofMinimalAxioms
+      (fun _ _ _ => ext fun _ => smul_add _ _ _)
+      (fun _ _ _ => ext fun _ => add_smul _ _ _)
+      (fun _ _ _ => ext fun _ => mul_smul _ _ _)
+      (fun f => ext fun x => one_smul 𝕜 (f x))
 #align bounded_continuous_function.module' BoundedContinuousFunction.module'
 
 /- TODO: When `NormedModule` has been added to `Analysis.NormedSpace.Basic`, this

This typeclass probably didn't exist yet when this was written.

Also cleans up some nearby style and comments.

@@ -1401,32 +1401,31 @@ functions from `α` to `β` is naturally a module over the algebra of bounded co
 functions from `α` to `𝕜`. -/
 
 
-instance hasSmul' : SMul (α →ᵇ 𝕜) (α →ᵇ β) :=
-  ⟨fun (f : α →ᵇ 𝕜) (g : α →ᵇ β) =>
+instance hasSmul' : SMul (α →ᵇ 𝕜) (α →ᵇ β) where
+  smul f g :=
     ofNormedAddCommGroup (fun x => f x • g x) (f.continuous.smul g.continuous) (‖f‖ * ‖g‖) fun x =>
       calc
         ‖f x • g x‖ ≤ ‖f x‖ * ‖g x‖ := norm_smul_le _ _
         _ ≤ ‖f‖ * ‖g‖ :=
           mul_le_mul (f.norm_coe_le_norm _) (g.norm_coe_le_norm _) (norm_nonneg _) (norm_nonneg _)
-        ⟩
 #align bounded_continuous_function.has_smul' BoundedContinuousFunction.hasSmul'
 
 instance module' : Module (α →ᵇ 𝕜) (α →ᵇ β) :=
   Module.ofCore <|
-    { smul := (· • ·)
-      smul_add := fun _ _ _ => ext fun _ => smul_add _ _ _
+    { smul_add := fun _ _ _ => ext fun _ => smul_add _ _ _
       add_smul := fun _ _ _ => ext fun _ => add_smul _ _ _
       mul_smul := fun _ _ _ => ext fun _ => mul_smul _ _ _
       one_smul := fun f => ext fun x => one_smul 𝕜 (f x) }
 #align bounded_continuous_function.module' BoundedContinuousFunction.module'
 
-theorem norm_smul_le (f : α →ᵇ 𝕜) (g : α →ᵇ β) : ‖f • g‖ ≤ ‖f‖ * ‖g‖ :=
-  norm_ofNormedAddCommGroup_le _ (mul_nonneg (norm_nonneg _) (norm_nonneg _)) _
-#align bounded_continuous_function.norm_smul_le BoundedContinuousFunction.norm_smul_le
-
-/- TODO: When `NormedModule` has been added to `Analysis.NormedSpace.Basic`, the above facts
-show that the space of bounded continuous functions from `α` to `β` is naturally a normed
+/- TODO: When `NormedModule` has been added to `Analysis.NormedSpace.Basic`, this
+shows that the space of bounded continuous functions from `α` to `β` is naturally a normed
 module over the algebra of bounded continuous functions from `α` to `𝕜`. -/
+instance : BoundedSMul (α →ᵇ 𝕜) (α →ᵇ β) :=
+  BoundedSMul.of_norm_smul_le fun _ _ =>
+    norm_ofNormedAddCommGroup_le _ (mul_nonneg (norm_nonneg _) (norm_nonneg _)) _
+#align bounded_continuous_function.norm_smul_le norm_smul_le
+
 end NormedAlgebra
 
 theorem NNReal.upper_bound {α : Type*} [TopologicalSpace α] (f : α →ᵇ ℝ≥0) (x : α) :

@@ -767,7 +767,7 @@ open BigOperators
 @[simp]
 theorem coe_sum {ι : Type*} (s : Finset ι) (f : ι → α →ᵇ β) :
     ⇑(∑ i in s, f i) = ∑ i in s, (f i : α → β) :=
-  (@coeFnAddHom α β _ _ _ _).map_sum f s
+  map_sum coeFnAddHom f s
 #align bounded_continuous_function.coe_sum BoundedContinuousFunction.coe_sum
 
 theorem sum_apply {ι : Type*} (s : Finset ι) (f : ι → α →ᵇ β) (a : α) :

Use .asFn and .lemmasOnly as simps configuration options.

For reference, these are defined here:

https://github.com/leanprover-community/mathlib4/blob/4055c8b471380825f07416b12cb0cf266da44d84/Mathlib/Tactic/Simps/Basic.lean#L843-L851

@@ -291,7 +291,7 @@ theorem embedding_coeFn : Embedding (UniformFun.ofFun ∘ (⇑) : (α →ᵇ β)
 variable (α)
 
 /-- Constant as a continuous bounded function. -/
-@[simps! (config := { fullyApplied := false })] -- Porting note: Changed `simps` to `simps!`
+@[simps! (config := .asFn)] -- Porting note: Changed `simps` to `simps!`
 def const (b : β) : α →ᵇ β :=
   ⟨ContinuousMap.const α b, 0, by simp [le_rfl]⟩
 #align bounded_continuous_function.const BoundedContinuousFunction.const

Replace rcases( with rcases (. Same thing for convert( and congrm(. No other change.

@@ -354,7 +354,7 @@ instance [CompleteSpace β] : CompleteSpace (α →ᵇ β) :=
         exact lt_of_le_of_lt (fF_bdd x n) hn
       exact this.continuous (eventually_of_forall fun N => (f N).continuous)
     · -- Check that `F` is bounded
-      rcases(f 0).bounded with ⟨C, hC⟩
+      rcases (f 0).bounded with ⟨C, hC⟩
       refine' ⟨C + (b 0 + b 0), fun x y => _⟩
       calc
         dist (F x) (F y) ≤ dist (f 0 x) (f 0 y) + (dist (f 0 x) (F x) + dist (f 0 y) (F y)) :=

This PR adds some lemmas about integrals of bounded continuous functions. The lemmas are collected in a separate file.

Co-authored-by: kkytola <39528102+kkytola@users.noreply.github.com>

@@ -819,6 +819,12 @@ theorem norm_coe_le_norm (x : α) : ‖f x‖ ≤ ‖f‖ :=
     _ ≤ ‖f‖ := dist_coe_le_dist _
 #align bounded_continuous_function.norm_coe_le_norm BoundedContinuousFunction.norm_coe_le_norm
 
+lemma neg_norm_le_apply (f : α →ᵇ ℝ) (x : α) :
+    -‖f‖ ≤ f x := (abs_le.mp (norm_coe_le_norm f x)).1
+
+lemma apply_le_norm (f : α →ᵇ ℝ) (x : α) :
+    f x ≤ ‖f‖ := (abs_le.mp (norm_coe_le_norm f x)).2
+
 theorem dist_le_two_norm' {f : γ → β} {C : ℝ} (hC : ∀ x, ‖f x‖ ≤ C) (x y : γ) :
     dist (f x) (f y) ≤ 2 * C :=
   calc
@@ -1423,12 +1429,12 @@ show that the space of bounded continuous functions from `α` to `β` is natural
 module over the algebra of bounded continuous functions from `α` to `𝕜`. -/
 end NormedAlgebra
 
-theorem Nnreal.upper_bound {α : Type*} [TopologicalSpace α] (f : α →ᵇ ℝ≥0) (x : α) :
+theorem NNReal.upper_bound {α : Type*} [TopologicalSpace α] (f : α →ᵇ ℝ≥0) (x : α) :
     f x ≤ nndist f 0 := by
   have key : nndist (f x) ((0 : α →ᵇ ℝ≥0) x) ≤ nndist f 0 := @dist_coe_le_dist α ℝ≥0 _ _ f 0 x
   simp only [coe_zero, Pi.zero_apply] at key
   rwa [NNReal.nndist_zero_eq_val' (f x)] at key
-#align bounded_continuous_function.nnreal.upper_bound BoundedContinuousFunction.Nnreal.upper_bound
+#align bounded_continuous_function.nnreal.upper_bound BoundedContinuousFunction.NNReal.upper_bound
 
 /-!
 ### Star structures
@@ -1623,4 +1629,22 @@ theorem abs_self_eq_nnrealPart_add_nnrealPart_neg (f : α →ᵇ ℝ) :
 
 end NonnegativePart
 
+section
+
+variable {α : Type*} [TopologicalSpace α]
+
+lemma add_norm_nonneg (f : α →ᵇ ℝ) :
+    0 ≤ f + const _ ‖f‖ := by
+  intro x
+  dsimp
+  linarith [(abs_le.mp (norm_coe_le_norm f x)).1]
+
+lemma norm_sub_nonneg (f : α →ᵇ ℝ) :
+    0 ≤ const _ ‖f‖ - f := by
+  intro x
+  dsimp
+  linarith [(abs_le.mp (norm_coe_le_norm f x)).2]
+
+end
+
 end BoundedContinuousFunction

As discussed on Zulip.

Co-authored-by: grunweg <grunweg@posteo.de>

@@ -587,7 +587,7 @@ theorem arzela_ascoli₂ (s : Set β) (hs : IsCompact s) (A : Set (α →ᵇ β)
   using compactness there and then lifting everything to the original space. -/
   have M : LipschitzWith 1 (↑) := LipschitzWith.subtype_val s
   let F : (α →ᵇ s) → α →ᵇ β := comp (↑) M
-  refine' isCompact_of_isClosed_subset ((_ : IsCompact (F ⁻¹' A)).image (continuous_comp M)) closed
+  refine' IsCompact.of_isClosed_subset ((_ : IsCompact (F ⁻¹' A)).image (continuous_comp M)) closed
       fun f hf => _
   · haveI : CompactSpace s := isCompact_iff_compactSpace.1 hs
     refine' arzela_ascoli₁ _ (continuous_iff_isClosed.1 (continuous_comp M) _ closed) _

Use Bornology.IsBounded instead.

@@ -23,7 +23,7 @@ the uniform distance.
 
 noncomputable section
 
-open Topology Classical NNReal uniformity UniformConvergence
+open Topology Bornology Classical NNReal uniformity UniformConvergence
 
 open Set Filter Metric Function
 
@@ -113,13 +113,13 @@ theorem ext (h : ∀ x, f x = g x) : f = g :=
   FunLike.ext _ _ h
 #align bounded_continuous_function.ext BoundedContinuousFunction.ext
 
-theorem bounded_range (f : α →ᵇ β) : Bounded (range f) :=
-  bounded_range_iff.2 f.bounded
-#align bounded_continuous_function.bounded_range BoundedContinuousFunction.bounded_range
+theorem isBounded_range (f : α →ᵇ β) : IsBounded (range f) :=
+  isBounded_range_iff.2 f.bounded
+#align bounded_continuous_function.bounded_range BoundedContinuousFunction.isBounded_range
 
-theorem bounded_image (f : α →ᵇ β) (s : Set α) : Bounded (f '' s) :=
-  f.bounded_range.mono <| image_subset_range _ _
-#align bounded_continuous_function.bounded_image BoundedContinuousFunction.bounded_image
+theorem isBounded_image (f : α →ᵇ β) (s : Set α) : IsBounded (f '' s) :=
+  f.isBounded_range.subset <| image_subset_range _ _
+#align bounded_continuous_function.bounded_image BoundedContinuousFunction.isBounded_image
 
 theorem eq_of_empty [h : IsEmpty α] (f g : α →ᵇ β) : f = g :=
   ext <| h.elim
@@ -136,7 +136,7 @@ theorem mkOfBound_coe {f} {C} {h} : (mkOfBound f C h : α → β) = (f : α →
 
 /-- A continuous function on a compact space is automatically a bounded continuous function. -/
 def mkOfCompact [CompactSpace α] (f : C(α, β)) : α →ᵇ β :=
-  ⟨f, bounded_range_iff.1 (isCompact_range f.continuous).bounded⟩
+  ⟨f, isBounded_range_iff.1 (isCompact_range f.continuous).isBounded⟩
 #align bounded_continuous_function.mk_of_compact BoundedContinuousFunction.mkOfCompact
 
 @[simp]
@@ -159,8 +159,8 @@ theorem dist_eq : dist f g = sInf { C | 0 ≤ C ∧ ∀ x : α, dist (f x) (g x)
 #align bounded_continuous_function.dist_eq BoundedContinuousFunction.dist_eq
 
 theorem dist_set_exists : ∃ C, 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C := by
-  rcases f.bounded_range.union g.bounded_range with ⟨C, hC⟩
-  refine' ⟨max 0 C, le_max_left _ _, fun x => (hC _ _ _ _).trans (le_max_right _ _)⟩
+  rcases isBounded_iff.1 (f.isBounded_range.union g.isBounded_range) with ⟨C, hC⟩
+  refine' ⟨max 0 C, le_max_left _ _, fun x => (hC _ _).trans (le_max_right _ _)⟩
     <;> [left; right]
     <;> apply mem_range_self
 #align bounded_continuous_function.dist_set_exists BoundedContinuousFunction.dist_set_exists
@@ -454,8 +454,8 @@ nonrec def extend (f : α ↪ δ) (g : α →ᵇ β) (h : δ →ᵇ β) : δ →
   toFun := extend f g h
   continuous_toFun := continuous_of_discreteTopology
   map_bounded' := by
-    rw [← bounded_range_iff, range_extend f.injective, Metric.bounded_union]
-    exact ⟨g.bounded_range, h.bounded_image _⟩
+    rw [← isBounded_range_iff, range_extend f.injective]
+    exact g.isBounded_range.union (h.isBounded_image _)
 #align bounded_continuous_function.extend BoundedContinuousFunction.extend
 
 @[simp]
@@ -916,7 +916,7 @@ theorem norm_normComp : ‖f.normComp‖ = ‖f‖ := by
 #align bounded_continuous_function.norm_norm_comp BoundedContinuousFunction.norm_normComp
 
 theorem bddAbove_range_norm_comp : BddAbove <| Set.range <| norm ∘ f :=
-  (Real.bounded_iff_bddBelow_bddAbove.mp <| @bounded_range _ _ _ _ f.normComp).2
+  (Real.isBounded_iff_bddBelow_bddAbove.mp <| @isBounded_range _ _ _ _ f.normComp).2
 #align bounded_continuous_function.bdd_above_range_norm_comp BoundedContinuousFunction.bddAbove_range_norm_comp
 
 theorem norm_eq_iSup_norm : ‖f‖ = ⨆ x : α, ‖f x‖ := by

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

This has nice performance benefits.

@@ -29,13 +29,13 @@ open Set Filter Metric Function
 
 universe u v w
 
-variable {F : Type _} {α : Type u} {β : Type v} {γ : Type w}
+variable {F : Type*} {α : Type u} {β : Type v} {γ : Type w}
 
 /-- `α →ᵇ β` is the type of bounded continuous functions `α → β` from a topological space to a
 metric space.
 
 When possible, instead of parametrizing results over `(f : α →ᵇ β)`,
-you should parametrize over `(F : Type _) [BoundedContinuousMapClass F α β] (f : F)`.
+you should parametrize over `(F : Type*) [BoundedContinuousMapClass F α β] (f : F)`.
 
 When you extend this structure, make sure to extend `BoundedContinuousMapClass`. -/
 structure BoundedContinuousFunction (α : Type u) (β : Type v) [TopologicalSpace α]
@@ -48,11 +48,11 @@ scoped[BoundedContinuousFunction] infixr:25 " →ᵇ " => BoundedContinuousFunct
 
 section
 
--- Porting note: Changed type of `α β` from `Type _` to `outParam <| Type _`.
+-- Porting note: Changed type of `α β` from `Type*` to `outParam <| Type*`.
 /-- `BoundedContinuousMapClass F α β` states that `F` is a type of bounded continuous maps.
 
 You should also extend this typeclass when you extend `BoundedContinuousFunction`. -/
-class BoundedContinuousMapClass (F : Type _) (α β : outParam <| Type _) [TopologicalSpace α]
+class BoundedContinuousMapClass (F : Type*) (α β : outParam <| Type*) [TopologicalSpace α]
     [PseudoMetricSpace β] extends ContinuousMapClass F α β where
   map_bounded (f : F) : ∃ C, ∀ x y, dist (f x) (f y) ≤ C
 #align bounded_continuous_map_class BoundedContinuousMapClass
@@ -257,7 +257,7 @@ theorem nndist_eq_iSup : nndist f g = ⨆ x : α, nndist (f x) (g x) :=
   Subtype.ext <| dist_eq_iSup.trans <| by simp_rw [val_eq_coe, coe_iSup, coe_nndist]
 #align bounded_continuous_function.nndist_eq_supr BoundedContinuousFunction.nndist_eq_iSup
 
-theorem tendsto_iff_tendstoUniformly {ι : Type _} {F : ι → α →ᵇ β} {f : α →ᵇ β} {l : Filter ι} :
+theorem tendsto_iff_tendstoUniformly {ι : Type*} {F : ι → α →ᵇ β} {f : α →ᵇ β} {l : Filter ι} :
     Tendsto F l (𝓝 f) ↔ TendstoUniformly (fun i => F i) f l :=
   Iff.intro
     (fun h =>
@@ -366,27 +366,27 @@ instance [CompleteSpace β] : CompleteSpace (α →ᵇ β) :=
       exact fun N => (dist_le (b0 _)).2 fun x => fF_bdd x N
 
 /-- Composition of a bounded continuous function and a continuous function. -/
-def compContinuous {δ : Type _} [TopologicalSpace δ] (f : α →ᵇ β) (g : C(δ, α)) : δ →ᵇ β where
+def compContinuous {δ : Type*} [TopologicalSpace δ] (f : α →ᵇ β) (g : C(δ, α)) : δ →ᵇ β where
   toContinuousMap := f.1.comp g
   map_bounded' := f.map_bounded'.imp fun _ hC _ _ => hC _ _
 #align bounded_continuous_function.comp_continuous BoundedContinuousFunction.compContinuous
 
 @[simp]
-theorem coe_compContinuous {δ : Type _} [TopologicalSpace δ] (f : α →ᵇ β) (g : C(δ, α)) :
+theorem coe_compContinuous {δ : Type*} [TopologicalSpace δ] (f : α →ᵇ β) (g : C(δ, α)) :
     ⇑(f.compContinuous g) = f ∘ g := rfl
 #align bounded_continuous_function.coe_comp_continuous BoundedContinuousFunction.coe_compContinuous
 
 @[simp]
-theorem compContinuous_apply {δ : Type _} [TopologicalSpace δ] (f : α →ᵇ β) (g : C(δ, α)) (x : δ) :
+theorem compContinuous_apply {δ : Type*} [TopologicalSpace δ] (f : α →ᵇ β) (g : C(δ, α)) (x : δ) :
     f.compContinuous g x = f (g x) := rfl
 #align bounded_continuous_function.comp_continuous_apply BoundedContinuousFunction.compContinuous_apply
 
-theorem lipschitz_compContinuous {δ : Type _} [TopologicalSpace δ] (g : C(δ, α)) :
+theorem lipschitz_compContinuous {δ : Type*} [TopologicalSpace δ] (g : C(δ, α)) :
     LipschitzWith 1 fun f : α →ᵇ β => f.compContinuous g :=
   LipschitzWith.mk_one fun _ _ => (dist_le dist_nonneg).2 fun x => dist_coe_le_dist (g x)
 #align bounded_continuous_function.lipschitz_comp_continuous BoundedContinuousFunction.lipschitz_compContinuous
 
-theorem continuous_compContinuous {δ : Type _} [TopologicalSpace δ] (g : C(δ, α)) :
+theorem continuous_compContinuous {δ : Type*} [TopologicalSpace δ] (g : C(δ, α)) :
     Continuous fun f : α →ᵇ β => f.compContinuous g :=
   (lipschitz_compContinuous g).continuous
 #align bounded_continuous_function.continuous_comp_continuous BoundedContinuousFunction.continuous_compContinuous
@@ -446,7 +446,7 @@ def codRestrict (s : Set β) (f : α →ᵇ β) (H : ∀ x, f x ∈ s) : α →
 
 section Extend
 
-variable {δ : Type _} [TopologicalSpace δ] [DiscreteTopology δ]
+variable {δ : Type*} [TopologicalSpace δ] [DiscreteTopology δ]
 
 /-- A version of `Function.extend` for bounded continuous maps. We assume that the domain has
 discrete topology, so we only need to verify boundedness. -/
@@ -765,12 +765,12 @@ instance : AddCommMonoid (α →ᵇ β) :=
 open BigOperators
 
 @[simp]
-theorem coe_sum {ι : Type _} (s : Finset ι) (f : ι → α →ᵇ β) :
+theorem coe_sum {ι : Type*} (s : Finset ι) (f : ι → α →ᵇ β) :
     ⇑(∑ i in s, f i) = ∑ i in s, (f i : α → β) :=
   (@coeFnAddHom α β _ _ _ _).map_sum f s
 #align bounded_continuous_function.coe_sum BoundedContinuousFunction.coe_sum
 
-theorem sum_apply {ι : Type _} (s : Finset ι) (f : ι → α →ᵇ β) (a : α) :
+theorem sum_apply {ι : Type*} (s : Finset ι) (f : ι → α →ᵇ β) (a : α) :
     (∑ i in s, f i) a = ∑ i in s, f i a := by simp
 #align bounded_continuous_function.sum_apply BoundedContinuousFunction.sum_apply
 
@@ -1055,7 +1055,7 @@ functions from `α` to `β` inherits a so-called `BoundedSMul` structure (in par
 using pointwise operations and checking that they are compatible with the uniform distance. -/
 
 
-variable {𝕜 : Type _} [PseudoMetricSpace 𝕜] [TopologicalSpace α] [PseudoMetricSpace β]
+variable {𝕜 : Type*} [PseudoMetricSpace 𝕜] [TopologicalSpace α] [PseudoMetricSpace β]
 
 section SMul
 
@@ -1165,7 +1165,7 @@ continuous functions from `α` to `β` inherits a normed space structure, by usi
 pointwise operations and checking that they are compatible with the uniform distance. -/
 
 
-variable {𝕜 : Type _}
+variable {𝕜 : Type*}
 
 variable [TopologicalSpace α] [SeminormedAddCommGroup β]
 
@@ -1216,7 +1216,7 @@ continuous functions from `α` to `R` inherits a normed ring structure, by using
 pointwise operations and checking that they are compatible with the uniform distance. -/
 
 
-variable [TopologicalSpace α] {R : Type _}
+variable [TopologicalSpace α] {R : Type*}
 
 section NonUnital
 
@@ -1321,7 +1321,7 @@ continuous functions from `α` to `R` inherits a normed commutative ring structu
 pointwise operations and checking that they are compatible with the uniform distance. -/
 
 
-variable [TopologicalSpace α] {R : Type _}
+variable [TopologicalSpace α] {R : Type*}
 
 instance commRing [SeminormedCommRing R] : CommRing (α →ᵇ R) :=
   { BoundedContinuousFunction.ring with
@@ -1349,7 +1349,7 @@ continuous functions from `α` to `γ` inherits a normed algebra structure, by u
 pointwise operations and checking that they are compatible with the uniform distance. -/
 
 
-variable {𝕜 : Type _} [NormedField 𝕜]
+variable {𝕜 : Type*} [NormedField 𝕜]
 
 variable [TopologicalSpace α] [SeminormedAddCommGroup β] [NormedSpace 𝕜 β]
 
@@ -1423,7 +1423,7 @@ show that the space of bounded continuous functions from `α` to `β` is natural
 module over the algebra of bounded continuous functions from `α` to `𝕜`. -/
 end NormedAlgebra
 
-theorem Nnreal.upper_bound {α : Type _} [TopologicalSpace α] (f : α →ᵇ ℝ≥0) (x : α) :
+theorem Nnreal.upper_bound {α : Type*} [TopologicalSpace α] (f : α →ᵇ ℝ≥0) (x : α) :
     f x ≤ nndist f 0 := by
   have key : nndist (f x) ((0 : α →ᵇ ℝ≥0) x) ≤ nndist f 0 := @dist_coe_le_dist α ℝ≥0 _ _ f 0 x
   simp only [coe_zero, Pi.zero_apply] at key
@@ -1450,7 +1450,7 @@ completeness is guaranteed when `β` is complete (see
 
 section NormedAddCommGroup
 
-variable {𝕜 : Type _} [NormedField 𝕜] [StarRing 𝕜] [TopologicalSpace α] [SeminormedAddCommGroup β]
+variable {𝕜 : Type*} [NormedField 𝕜] [StarRing 𝕜] [TopologicalSpace α] [SeminormedAddCommGroup β]
   [StarAddMonoid β] [NormedStarGroup β]
 
 variable [NormedSpace 𝕜 β] [StarModule 𝕜 β]

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Mario Carneiro, Yury Kudryashov, Heather Macbeth
-
-! This file was ported from Lean 3 source module topology.continuous_function.bounded
-! leanprover-community/mathlib commit 5dc275ec639221ca4d5f56938eb966f6ad9bc89f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Normed.Order.Lattice
 import Mathlib.Analysis.NormedSpace.OperatorNorm
@@ -15,6 +10,8 @@ import Mathlib.Data.Real.Sqrt
 import Mathlib.Topology.ContinuousFunction.Algebra
 import Mathlib.Topology.MetricSpace.Equicontinuity
 
+#align_import topology.continuous_function.bounded from "leanprover-community/mathlib"@"5dc275ec639221ca4d5f56938eb966f6ad9bc89f"
+
 /-!
 # Bounded continuous functions
 

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -483,16 +483,16 @@ theorem extend_of_empty [IsEmpty α] (f : α ↪ δ) (g : α →ᵇ β) (h : δ
 @[simp]
 theorem dist_extend_extend (f : α ↪ δ) (g₁ g₂ : α →ᵇ β) (h₁ h₂ : δ →ᵇ β) :
     dist (g₁.extend f h₁) (g₂.extend f h₂) =
-      max (dist g₁ g₂) (dist (h₁.restrict (range fᶜ)) (h₂.restrict (range fᶜ))) := by
+      max (dist g₁ g₂) (dist (h₁.restrict (range f)ᶜ) (h₂.restrict (range f)ᶜ)) := by
   refine' le_antisymm ((dist_le <| le_max_iff.2 <| Or.inl dist_nonneg).2 fun x => _) (max_le _ _)
   · rcases _root_.em (∃ y, f y = x) with (⟨x, rfl⟩ | hx)
     · simp only [extend_apply]
       exact (dist_coe_le_dist x).trans (le_max_left _ _)
     · simp only [extend_apply' hx]
-      lift x to (range fᶜ : Set δ) using hx
+      lift x to ((range f)ᶜ : Set δ) using hx
       calc
-        dist (h₁ x) (h₂ x) = dist (h₁.restrict (range fᶜ) x) (h₂.restrict (range fᶜ) x) := rfl
-        _ ≤ dist (h₁.restrict (range fᶜ)) (h₂.restrict (range fᶜ)) := (dist_coe_le_dist x)
+        dist (h₁ x) (h₂ x) = dist (h₁.restrict (range f)ᶜ x) (h₂.restrict (range f)ᶜ x) := rfl
+        _ ≤ dist (h₁.restrict (range f)ᶜ) (h₂.restrict (range f)ᶜ) := (dist_coe_le_dist x)
         _ ≤ _ := le_max_right _ _
   · refine' (dist_le dist_nonneg).2 fun x => _
     rw [← extend_apply f g₁ h₁, ← extend_apply f g₂ h₂]

• It suffices to require continuity in the second argument for the first argument from a dense set.
• Rename lemmas to include lipschitzWith/lipschitzWithOn.

@@ -329,7 +329,7 @@ theorem continuous_eval_const {x : α} : Continuous fun f : α →ᵇ β => f x
 /-- The evaluation map is continuous, as a joint function of `u` and `x`. -/
 @[continuity]
 theorem continuous_eval : Continuous fun p : (α →ᵇ β) × α => p.1 p.2 :=
-  (continuous_prod_of_continuous_lipschitz _ 1 fun f => f.continuous) <| lipschitz_evalx
+  (continuous_prod_of_continuous_lipschitzWith _ 1 fun f => f.continuous) <| lipschitz_evalx
 #align bounded_continuous_function.continuous_eval BoundedContinuousFunction.continuous_eval
 
 /-- Bounded continuous functions taking values in a complete space form a complete space. -/

Changes are of the form

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

@@ -1528,7 +1528,7 @@ instance semilatticeInf : SemilatticeInf (α →ᵇ β) :=
           obtain ⟨C₁, hf⟩ := f.bounded
           obtain ⟨C₂, hg⟩ := g.bounded
           refine' ⟨C₁ + C₂, fun x y => _⟩
-          simp_rw [NormedAddCommGroup.dist_eq] at hf hg⊢
+          simp_rw [NormedAddCommGroup.dist_eq] at hf hg ⊢
           exact (norm_inf_sub_inf_le_add_norm _ _ _ _).trans (add_le_add (hf _ _) (hg _ _)) }
     inf_le_left := fun f g => ContinuousMap.le_def.mpr fun _ => inf_le_left
     inf_le_right := fun f g => ContinuousMap.le_def.mpr fun _ => inf_le_right
@@ -1545,7 +1545,7 @@ instance semilatticeSup : SemilatticeSup (α →ᵇ β) :=
           obtain ⟨C₁, hf⟩ := f.bounded
           obtain ⟨C₂, hg⟩ := g.bounded
           refine' ⟨C₁ + C₂, fun x y => _⟩
-          simp_rw [NormedAddCommGroup.dist_eq] at hf hg⊢
+          simp_rw [NormedAddCommGroup.dist_eq] at hf hg ⊢
           exact (norm_sup_sub_sup_le_add_norm _ _ _ _).trans (add_le_add (hf _ _) (hg _ _)) }
     le_sup_left := fun f g => ContinuousMap.le_def.mpr fun _ => le_sup_left
     le_sup_right := fun f g => ContinuousMap.le_def.mpr fun _ => le_sup_right

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

@@ -415,8 +415,8 @@ def comp (G : β → γ) {C : ℝ≥0} (H : LipschitzWith C G) (f : α →ᵇ β
     ⟨max C 0 * D, fun x y =>
       calc
         dist (G (f x)) (G (f y)) ≤ C * dist (f x) (f y) := H.dist_le_mul _ _
-        _ ≤ max C 0 * dist (f x) (f y) := (mul_le_mul_of_nonneg_right (le_max_left C 0) dist_nonneg)
-        _ ≤ max C 0 * D := mul_le_mul_of_nonneg_left (hD _ _) (le_max_right C 0)
+        _ ≤ max C 0 * dist (f x) (f y) := by gcongr; apply le_max_left
+        _ ≤ max C 0 * D := by gcongr; apply hD
         ⟩⟩
 #align bounded_continuous_function.comp BoundedContinuousFunction.comp
 
@@ -427,7 +427,7 @@ theorem lipschitz_comp {G : β → γ} {C : ℝ≥0} (H : LipschitzWith C G) :
     (dist_le (mul_nonneg C.2 dist_nonneg)).2 fun x =>
       calc
         dist (G (f x)) (G (g x)) ≤ C * dist (f x) (g x) := H.dist_le_mul _ _
-        _ ≤ C * dist f g := mul_le_mul_of_nonneg_left (dist_coe_le_dist _) C.2
+        _ ≤ C * dist f g := by gcongr; apply dist_coe_le_dist
 #align bounded_continuous_function.lipschitz_comp BoundedContinuousFunction.lipschitz_comp
 
 /-- The composition operator (in the target) with a Lipschitz map is uniformly continuous. -/

The main breaking change is that tac <;> [t1, t2] is now written tac <;> [t1; t2], to avoid clashing with tactics like cases and use that take comma-separated lists.

@@ -164,7 +164,7 @@ theorem dist_eq : dist f g = sInf { C | 0 ≤ C ∧ ∀ x : α, dist (f x) (g x)
 theorem dist_set_exists : ∃ C, 0 ≤ C ∧ ∀ x : α, dist (f x) (g x) ≤ C := by
   rcases f.bounded_range.union g.bounded_range with ⟨C, hC⟩
   refine' ⟨max 0 C, le_max_left _ _, fun x => (hC _ _ _ _).trans (le_max_right _ _)⟩
-    <;> [left, right]
+    <;> [left; right]
     <;> apply mem_range_self
 #align bounded_continuous_function.dist_set_exists BoundedContinuousFunction.dist_set_exists
 

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