measure_theory.integral.riesz_markov_kakutani ⟷ Mathlib.MeasureTheory.Integral.RieszMarkovKakutani

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

@@ -3,8 +3,8 @@ Copyright (c) 2022 Jesse Reimann. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jesse Reimann, Kalle Kytölä
 -/
-import Mathbin.Topology.ContinuousFunction.Bounded
-import Mathbin.Topology.Sets.Compacts
+import Topology.ContinuousFunction.Bounded
+import Topology.Sets.Compacts
 
 #align_import measure_theory.integral.riesz_markov_kakutani from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
 

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

@@ -52,17 +52,17 @@ def rieszContentAux : Compacts X → ℝ≥0 := fun K =>
 
 section RieszMonotone
 
-#print riesz_content_aux_image_nonempty /-
+#print rieszContentAux_image_nonempty /-
 /-- For any compact subset `K ⊆ X`, there exist some bounded continuous nonnegative
 functions f on X such that `f ≥ 1` on K. -/
-theorem riesz_content_aux_image_nonempty (K : Compacts X) :
+theorem rieszContentAux_image_nonempty (K : Compacts X) :
     (Λ '' {f : X →ᵇ ℝ≥0 | ∀ x ∈ K, (1 : ℝ≥0) ≤ f x}).Nonempty :=
   by
   rw [nonempty_image_iff]
   use(1 : X →ᵇ ℝ≥0)
   intro x x_in_K
   simp only [BoundedContinuousFunction.coe_one, Pi.one_apply]
-#align riesz_content_aux_image_nonempty riesz_content_aux_image_nonempty
+#align riesz_content_aux_image_nonempty rieszContentAux_image_nonempty
 -/
 
 #print rieszContentAux_mono /-
@@ -70,7 +70,7 @@ theorem riesz_content_aux_image_nonempty (K : Compacts X) :
 monotone: if `K₁ ⊆ K₂` are compact subsets in X, then `λ(K₁) ≤ λ(K₂)`. -/
 theorem rieszContentAux_mono {K₁ K₂ : Compacts X} (h : K₁ ≤ K₂) :
     rieszContentAux Λ K₁ ≤ rieszContentAux Λ K₂ :=
-  csInf_le_csInf (OrderBot.bddBelow _) (riesz_content_aux_image_nonempty Λ K₂)
+  csInf_le_csInf (OrderBot.bddBelow _) (rieszContentAux_image_nonempty Λ K₂)
     (image_subset Λ (setOf_subset_setOf.mpr fun f f_hyp x x_in_K₁ => f_hyp x (h x_in_K₁)))
 #align riesz_content_aux_mono rieszContentAux_mono
 -/
@@ -97,7 +97,7 @@ theorem exists_lt_rieszContentAux_add_pos (K : Compacts X) {ε : ℝ≥0} (εpos
   by
   --choose a test function `f` s.t. `Λf = α < λ(K) + ε`
   obtain ⟨α, ⟨⟨f, f_hyp⟩, α_hyp⟩⟩ :=
-    exists_lt_of_csInf_lt (riesz_content_aux_image_nonempty Λ K)
+    exists_lt_of_csInf_lt (rieszContentAux_image_nonempty Λ K)
       (lt_add_of_pos_right (rieszContentAux Λ K) εpos)
   refine' ⟨f, f_hyp.left, _⟩
   rw [f_hyp.right]

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

@@ -59,7 +59,7 @@ theorem riesz_content_aux_image_nonempty (K : Compacts X) :
     (Λ '' {f : X →ᵇ ℝ≥0 | ∀ x ∈ K, (1 : ℝ≥0) ≤ f x}).Nonempty :=
   by
   rw [nonempty_image_iff]
-  use (1 : X →ᵇ ℝ≥0)
+  use(1 : X →ᵇ ℝ≥0)
   intro x x_in_K
   simp only [BoundedContinuousFunction.coe_one, Pi.one_apply]
 #align riesz_content_aux_image_nonempty riesz_content_aux_image_nonempty

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Jesse Reimann. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jesse Reimann, Kalle Kytölä
-
-! This file was ported from Lean 3 source module measure_theory.integral.riesz_markov_kakutani
-! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.ContinuousFunction.Bounded
 import Mathbin.Topology.Sets.Compacts
 
+#align_import measure_theory.integral.riesz_markov_kakutani from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
+
 /-!
 #  Riesz–Markov–Kakutani representation theorem
 

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

@@ -44,15 +44,18 @@ variable (Λ : (X →ᵇ ℝ≥0) →ₗ[ℝ≥0] ℝ≥0)
 /-! ### Construction of the content: -/
 
 
+#print rieszContentAux /-
 /-- Given a positive linear functional Λ on X, for `K ⊆ X` compact define
 `λ(K) = inf {Λf | 1≤f on K}`. When X is a compact Hausdorff space, this will be shown to be a
 content, and will be shown to agree with the Riesz measure on the compact subsets `K ⊆ X`. -/
 def rieszContentAux : Compacts X → ℝ≥0 := fun K =>
   sInf (Λ '' {f : X →ᵇ ℝ≥0 | ∀ x ∈ K, (1 : ℝ≥0) ≤ f x})
 #align riesz_content_aux rieszContentAux
+-/
 
 section RieszMonotone
 
+#print riesz_content_aux_image_nonempty /-
 /-- For any compact subset `K ⊆ X`, there exist some bounded continuous nonnegative
 functions f on X such that `f ≥ 1` on K. -/
 theorem riesz_content_aux_image_nonempty (K : Compacts X) :
@@ -63,7 +66,9 @@ theorem riesz_content_aux_image_nonempty (K : Compacts X) :
   intro x x_in_K
   simp only [BoundedContinuousFunction.coe_one, Pi.one_apply]
 #align riesz_content_aux_image_nonempty riesz_content_aux_image_nonempty
+-/
 
+#print rieszContentAux_mono /-
 /-- Riesz content λ (associated with a positive linear functional Λ) is
 monotone: if `K₁ ⊆ K₂` are compact subsets in X, then `λ(K₁) ≤ λ(K₂)`. -/
 theorem rieszContentAux_mono {K₁ K₂ : Compacts X} (h : K₁ ≤ K₂) :
@@ -71,18 +76,22 @@ theorem rieszContentAux_mono {K₁ K₂ : Compacts X} (h : K₁ ≤ K₂) :
   csInf_le_csInf (OrderBot.bddBelow _) (riesz_content_aux_image_nonempty Λ K₂)
     (image_subset Λ (setOf_subset_setOf.mpr fun f f_hyp x x_in_K₁ => f_hyp x (h x_in_K₁)))
 #align riesz_content_aux_mono rieszContentAux_mono
+-/
 
 end RieszMonotone
 
 section RieszSubadditive
 
+#print rieszContentAux_le /-
 /-- Any bounded continuous nonnegative f such that `f ≥ 1` on K gives an upper bound on the
 content of K; namely `λ(K) ≤ Λ f`. -/
 theorem rieszContentAux_le {K : Compacts X} {f : X →ᵇ ℝ≥0} (h : ∀ x ∈ K, (1 : ℝ≥0) ≤ f x) :
     rieszContentAux Λ K ≤ Λ f :=
   csInf_le (OrderBot.bddBelow _) ⟨f, ⟨h, rfl⟩⟩
 #align riesz_content_aux_le rieszContentAux_le
+-/
 
+#print exists_lt_rieszContentAux_add_pos /-
 /-- The Riesz content can be approximated arbitrarily well by evaluating the positive linear
 functional on test functions: for any `ε > 0`, there exists a bounded continuous nonnegative
 function f on X such that `f ≥ 1` on K and such that `λ(K) ≤ Λ f < λ(K) + ε`. -/
@@ -97,7 +106,9 @@ theorem exists_lt_rieszContentAux_add_pos (K : Compacts X) {ε : ℝ≥0} (εpos
   rw [f_hyp.right]
   exact α_hyp
 #align exists_lt_riesz_content_aux_add_pos exists_lt_rieszContentAux_add_pos
+-/
 
+#print rieszContentAux_sup_le /-
 /-- The Riesz content λ associated to a given positive linear functional Λ is
 finitely subadditive: `λ(K₁ ∪ K₂) ≤ λ(K₁) + λ(K₂)` for any compact subsets `K₁, K₂ ⊆ X`. -/
 theorem rieszContentAux_sup_le (K1 K2 : Compacts X) :
@@ -121,6 +132,7 @@ theorem rieszContentAux_sup_le (K1 K2 : Compacts X) :
   apply lt_of_lt_of_le (add_lt_add f_test_function_K1.right f_test_function_K2.right) (le_of_eq _)
   rw [add_assoc, add_comm (ε / 2), add_assoc, add_halves ε, add_assoc]
 #align riesz_content_aux_sup_le rieszContentAux_sup_le
+-/
 
 end RieszSubadditive
 

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

@@ -48,7 +48,7 @@ variable (Λ : (X →ᵇ ℝ≥0) →ₗ[ℝ≥0] ℝ≥0)
 `λ(K) = inf {Λf | 1≤f on K}`. When X is a compact Hausdorff space, this will be shown to be a
 content, and will be shown to agree with the Riesz measure on the compact subsets `K ⊆ X`. -/
 def rieszContentAux : Compacts X → ℝ≥0 := fun K =>
-  sInf (Λ '' { f : X →ᵇ ℝ≥0 | ∀ x ∈ K, (1 : ℝ≥0) ≤ f x })
+  sInf (Λ '' {f : X →ᵇ ℝ≥0 | ∀ x ∈ K, (1 : ℝ≥0) ≤ f x})
 #align riesz_content_aux rieszContentAux
 
 section RieszMonotone
@@ -56,7 +56,7 @@ section RieszMonotone
 /-- For any compact subset `K ⊆ X`, there exist some bounded continuous nonnegative
 functions f on X such that `f ≥ 1` on K. -/
 theorem riesz_content_aux_image_nonempty (K : Compacts X) :
-    (Λ '' { f : X →ᵇ ℝ≥0 | ∀ x ∈ K, (1 : ℝ≥0) ≤ f x }).Nonempty :=
+    (Λ '' {f : X →ᵇ ℝ≥0 | ∀ x ∈ K, (1 : ℝ≥0) ≤ f x}).Nonempty :=
   by
   rw [nonempty_image_iff]
   use (1 : X →ᵇ ℝ≥0)

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

@@ -33,7 +33,7 @@ compact subsets of the space X, rather than the usual construction of open sets
 
 noncomputable section
 
-open BoundedContinuousFunction NNReal ENNReal
+open scoped BoundedContinuousFunction NNReal ENNReal
 
 open Set Function TopologicalSpace
 

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

@@ -44,12 +44,6 @@ variable (Λ : (X →ᵇ ℝ≥0) →ₗ[ℝ≥0] ℝ≥0)
 /-! ### Construction of the content: -/
 
 
-/- warning: riesz_content_aux -> rieszContentAux is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X], (LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) -> (TopologicalSpace.Compacts.{u1} X _inst_1) -> NNReal
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X], (LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) -> (TopologicalSpace.Compacts.{u1} X _inst_1) -> NNReal
-Case conversion may be inaccurate. Consider using '#align riesz_content_aux rieszContentAuxₓ'. -/
 /-- Given a positive linear functional Λ on X, for `K ⊆ X` compact define
 `λ(K) = inf {Λf | 1≤f on K}`. When X is a compact Hausdorff space, this will be shown to be a
 content, and will be shown to agree with the Riesz measure on the compact subsets `K ⊆ X`. -/
@@ -59,9 +53,6 @@ def rieszContentAux : Compacts X → ℝ≥0 := fun K =>
 
 section RieszMonotone
 
-/- warning: riesz_content_aux_image_nonempty -> riesz_content_aux_image_nonempty is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align riesz_content_aux_image_nonempty riesz_content_aux_image_nonemptyₓ'. -/
 /-- For any compact subset `K ⊆ X`, there exist some bounded continuous nonnegative
 functions f on X such that `f ≥ 1` on K. -/
 theorem riesz_content_aux_image_nonempty (K : Compacts X) :
@@ -73,12 +64,6 @@ theorem riesz_content_aux_image_nonempty (K : Compacts X) :
   simp only [BoundedContinuousFunction.coe_one, Pi.one_apply]
 #align riesz_content_aux_image_nonempty riesz_content_aux_image_nonempty
 
-/- warning: riesz_content_aux_mono -> rieszContentAux_mono is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) {K₁ : TopologicalSpace.Compacts.{u1} X _inst_1} {K₂ : TopologicalSpace.Compacts.{u1} X _inst_1}, (LE.le.{u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Preorder.toHasLe.{u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.setLike.{u1} X _inst_1)))) K₁ K₂) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (rieszContentAux.{u1} X _inst_1 Λ K₁) (rieszContentAux.{u1} X _inst_1 Λ K₂))
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) {K₁ : TopologicalSpace.Compacts.{u1} X _inst_1} {K₂ : TopologicalSpace.Compacts.{u1} X _inst_1}, (LE.le.{u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Preorder.toLE.{u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (SemilatticeSup.toPartialOrder.{u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (TopologicalSpace.Compacts.instSemilatticeSupCompacts.{u1} X _inst_1)))) K₁ K₂) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (rieszContentAux.{u1} X _inst_1 Λ K₁) (rieszContentAux.{u1} X _inst_1 Λ K₂))
-Case conversion may be inaccurate. Consider using '#align riesz_content_aux_mono rieszContentAux_monoₓ'. -/
 /-- Riesz content λ (associated with a positive linear functional Λ) is
 monotone: if `K₁ ⊆ K₂` are compact subsets in X, then `λ(K₁) ≤ λ(K₂)`. -/
 theorem rieszContentAux_mono {K₁ K₂ : Compacts X} (h : K₁ ≤ K₂) :
@@ -91,9 +76,6 @@ end RieszMonotone
 
 section RieszSubadditive
 
-/- warning: riesz_content_aux_le -> rieszContentAux_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align riesz_content_aux_le rieszContentAux_leₓ'. -/
 /-- Any bounded continuous nonnegative f such that `f ≥ 1` on K gives an upper bound on the
 content of K; namely `λ(K) ≤ Λ f`. -/
 theorem rieszContentAux_le {K : Compacts X} {f : X →ᵇ ℝ≥0} (h : ∀ x ∈ K, (1 : ℝ≥0) ≤ f x) :
@@ -101,9 +83,6 @@ theorem rieszContentAux_le {K : Compacts X} {f : X →ᵇ ℝ≥0} (h : ∀ x 
   csInf_le (OrderBot.bddBelow _) ⟨f, ⟨h, rfl⟩⟩
 #align riesz_content_aux_le rieszContentAux_le
 
-/- warning: exists_lt_riesz_content_aux_add_pos -> exists_lt_rieszContentAux_add_pos is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align exists_lt_riesz_content_aux_add_pos exists_lt_rieszContentAux_add_posₓ'. -/
 /-- The Riesz content can be approximated arbitrarily well by evaluating the positive linear
 functional on test functions: for any `ε > 0`, there exists a bounded continuous nonnegative
 function f on X such that `f ≥ 1` on K and such that `λ(K) ≤ Λ f < λ(K) + ε`. -/
@@ -119,12 +98,6 @@ theorem exists_lt_rieszContentAux_add_pos (K : Compacts X) {ε : ℝ≥0} (εpos
   exact α_hyp
 #align exists_lt_riesz_content_aux_add_pos exists_lt_rieszContentAux_add_pos
 
-/- warning: riesz_content_aux_sup_le -> rieszContentAux_sup_le is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) (K1 : TopologicalSpace.Compacts.{u1} X _inst_1) (K2 : TopologicalSpace.Compacts.{u1} X _inst_1), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (rieszContentAux.{u1} X _inst_1 Λ (Sup.sup.{u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (TopologicalSpace.Compacts.hasSup.{u1} X _inst_1) K1 K2)) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (rieszContentAux.{u1} X _inst_1 Λ K1) (rieszContentAux.{u1} X _inst_1 Λ K2))
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) (K1 : TopologicalSpace.Compacts.{u1} X _inst_1) (K2 : TopologicalSpace.Compacts.{u1} X _inst_1), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (rieszContentAux.{u1} X _inst_1 Λ (Sup.sup.{u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (TopologicalSpace.Compacts.instSupCompacts.{u1} X _inst_1) K1 K2)) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) (rieszContentAux.{u1} X _inst_1 Λ K1) (rieszContentAux.{u1} X _inst_1 Λ K2))
-Case conversion may be inaccurate. Consider using '#align riesz_content_aux_sup_le rieszContentAux_sup_leₓ'. -/
 /-- The Riesz content λ associated to a given positive linear functional Λ is
 finitely subadditive: `λ(K₁ ∪ K₂) ≤ λ(K₁) + λ(K₂)` for any compact subsets `K₁, K₂ ⊆ X`. -/
 theorem rieszContentAux_sup_le (K1 K2 : Compacts X) :

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

@@ -60,10 +60,7 @@ def rieszContentAux : Compacts X → ℝ≥0 := fun K =>
 section RieszMonotone
 
 /- warning: riesz_content_aux_image_nonempty -> riesz_content_aux_image_nonempty is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) (K : TopologicalSpace.Compacts.{u1} X _inst_1), Set.Nonempty.{0} NNReal (Set.image.{u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (coeFn.{succ u1, succ u1} (LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) (fun (_x : LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) => (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) -> NNReal) (LinearMap.hasCoeToFun.{0, 0, u1, 0} NNReal NNReal (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal NNReal.semiring NNReal.semiring (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring) (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Λ) (setOf.{u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (f : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) => forall (x : X), (Membership.Mem.{u1, u1} X (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.hasMem.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.setLike.{u1} X _inst_1)) x K) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) => X -> NNReal) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) f x)))))
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) (K : TopologicalSpace.Compacts.{u1} X _inst_1), Set.Nonempty.{0} NNReal (Set.image.{u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (FunLike.coe.{succ u1, succ u1, 1} (LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal 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(x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, 0} NNReal NNReal (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal instNNRealSemiring instNNRealSemiring (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring) (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Λ) (setOf.{u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) (fun (f : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => forall (x : X), (Membership.mem.{u1, u1} X (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.instMembership.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} X _inst_1)) x K) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X (fun (_x : X) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : X) => NNReal) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 (UniformSpace.toTopologicalSpace.{0} NNReal (PseudoMetricSpace.toUniformSpace.{0} NNReal instPseudoMetricSpaceNNReal)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 instPseudoMetricSpaceNNReal (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal))) f x)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align riesz_content_aux_image_nonempty riesz_content_aux_image_nonemptyₓ'. -/
 /-- For any compact subset `K ⊆ X`, there exist some bounded continuous nonnegative
 functions f on X such that `f ≥ 1` on K. -/
@@ -95,10 +92,7 @@ end RieszMonotone
 section RieszSubadditive
 
 /- warning: riesz_content_aux_le -> rieszContentAux_le is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) {K : TopologicalSpace.Compacts.{u1} X _inst_1} {f : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace}, (forall (x : X), (Membership.Mem.{u1, u1} X (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.hasMem.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.setLike.{u1} X _inst_1)) x K) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) => X -> NNReal) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) f x))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (rieszContentAux.{u1} X _inst_1 Λ K) (coeFn.{succ u1, succ u1} (LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) (fun (_x : LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) => (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) -> NNReal) (LinearMap.hasCoeToFun.{0, 0, u1, 0} NNReal NNReal (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal NNReal.semiring NNReal.semiring (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring) (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Λ f))
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) {K : TopologicalSpace.Compacts.{u1} X _inst_1} {f : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal}, (forall (x : X), (Membership.mem.{u1, u1} X (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.instMembership.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} X _inst_1)) x K) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X (fun (_x : X) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : X) => NNReal) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 (UniformSpace.toTopologicalSpace.{0} NNReal (PseudoMetricSpace.toUniformSpace.{0} NNReal instPseudoMetricSpaceNNReal)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 instPseudoMetricSpaceNNReal (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal))) f x))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (rieszContentAux.{u1} X _inst_1 Λ K) (FunLike.coe.{succ u1, succ u1, 1} (LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) (fun (_x : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, 0} NNReal NNReal (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal instNNRealSemiring instNNRealSemiring (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring) (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Λ f))
+<too large>
 Case conversion may be inaccurate. Consider using '#align riesz_content_aux_le rieszContentAux_leₓ'. -/
 /-- Any bounded continuous nonnegative f such that `f ≥ 1` on K gives an upper bound on the
 content of K; namely `λ(K) ≤ Λ f`. -/
@@ -108,10 +102,7 @@ theorem rieszContentAux_le {K : Compacts X} {f : X →ᵇ ℝ≥0} (h : ∀ x 
 #align riesz_content_aux_le rieszContentAux_le
 
 /- warning: exists_lt_riesz_content_aux_add_pos -> exists_lt_rieszContentAux_add_pos is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) (K : TopologicalSpace.Compacts.{u1} X _inst_1) {ε : NNReal}, (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) ε) -> (Exists.{succ u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (f : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) => And (forall (x : X), (Membership.Mem.{u1, u1} X (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.hasMem.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.setLike.{u1} X _inst_1)) x K) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) => X -> NNReal) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) f x))) (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (coeFn.{succ u1, succ u1} (LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) (fun (_x : LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) => (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) -> NNReal) (LinearMap.hasCoeToFun.{0, 0, u1, 0} NNReal NNReal (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal NNReal.semiring NNReal.semiring (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring) (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Λ f) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (rieszContentAux.{u1} X _inst_1 Λ K) ε))))
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) (K : TopologicalSpace.Compacts.{u1} X _inst_1) {ε : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) ε) -> (Exists.{succ u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) (fun (f : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => And (forall (x : X), (Membership.mem.{u1, u1} X (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.instMembership.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} X _inst_1)) x K) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X (fun (_x : X) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : X) => NNReal) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 (UniformSpace.toTopologicalSpace.{0} NNReal (PseudoMetricSpace.toUniformSpace.{0} NNReal instPseudoMetricSpaceNNReal)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 instPseudoMetricSpaceNNReal (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal))) f x))) (LT.lt.{0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) f) (Preorder.toLT.{0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) f) (PartialOrder.toPreorder.{0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) f) (StrictOrderedSemiring.toPartialOrder.{0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) f) instNNRealStrictOrderedSemiring))) (FunLike.coe.{succ u1, succ u1, 1} (LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) (fun (_x : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, 0} NNReal NNReal (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal instNNRealSemiring instNNRealSemiring (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring) (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Λ f) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) (rieszContentAux.{u1} X _inst_1 Λ K) ε))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align exists_lt_riesz_content_aux_add_pos exists_lt_rieszContentAux_add_posₓ'. -/
 /-- The Riesz content can be approximated arbitrarily well by evaluating the positive linear
 functional on test functions: for any `ε > 0`, there exists a bounded continuous nonnegative

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

@@ -63,7 +63,7 @@ section RieszMonotone
 lean 3 declaration is
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) (K : TopologicalSpace.Compacts.{u1} X _inst_1), Set.Nonempty.{0} NNReal (Set.image.{u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (coeFn.{succ u1, succ u1} (LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) (fun (_x : LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) => (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) -> NNReal) (LinearMap.hasCoeToFun.{0, 0, u1, 0} NNReal NNReal (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal NNReal.semiring NNReal.semiring (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring) (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Λ) (setOf.{u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (f : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) => forall (x : X), (Membership.Mem.{u1, u1} X (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.hasMem.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.setLike.{u1} X _inst_1)) x K) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) => X -> NNReal) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) f x)))))
 but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) (K : TopologicalSpace.Compacts.{u1} X _inst_1), Set.Nonempty.{0} NNReal (Set.image.{u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (FunLike.coe.{succ u1, succ u1, 1} (LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) (fun (_x : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, 0} NNReal NNReal (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal instNNRealSemiring instNNRealSemiring (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring) (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Λ) (setOf.{u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) (fun (f : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => forall (x : X), (Membership.mem.{u1, u1} X (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.instMembership.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} X _inst_1)) x K) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X (fun (_x : X) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : X) => NNReal) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 (UniformSpace.toTopologicalSpace.{0} NNReal (PseudoMetricSpace.toUniformSpace.{0} NNReal instPseudoMetricSpaceNNReal)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 instPseudoMetricSpaceNNReal (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal))) f x)))))
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) (K : TopologicalSpace.Compacts.{u1} X _inst_1), Set.Nonempty.{0} NNReal (Set.image.{u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (FunLike.coe.{succ u1, succ u1, 1} (LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) (fun (_x : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, 0} NNReal NNReal (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal instNNRealSemiring instNNRealSemiring (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring) (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Λ) (setOf.{u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) (fun (f : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => forall (x : X), (Membership.mem.{u1, u1} X (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.instMembership.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} X _inst_1)) x K) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X (fun (_x : X) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : X) => NNReal) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 (UniformSpace.toTopologicalSpace.{0} NNReal (PseudoMetricSpace.toUniformSpace.{0} NNReal instPseudoMetricSpaceNNReal)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 instPseudoMetricSpaceNNReal (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal))) f x)))))
 Case conversion may be inaccurate. Consider using '#align riesz_content_aux_image_nonempty riesz_content_aux_image_nonemptyₓ'. -/
 /-- For any compact subset `K ⊆ X`, there exist some bounded continuous nonnegative
 functions f on X such that `f ≥ 1` on K. -/
@@ -98,7 +98,7 @@ section RieszSubadditive
 lean 3 declaration is
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) {K : TopologicalSpace.Compacts.{u1} X _inst_1} {f : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace}, (forall (x : X), (Membership.Mem.{u1, u1} X (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.hasMem.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.setLike.{u1} X _inst_1)) x K) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) => X -> NNReal) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) f x))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (rieszContentAux.{u1} X _inst_1 Λ K) (coeFn.{succ u1, succ u1} (LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) (fun (_x : LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) => (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) -> NNReal) (LinearMap.hasCoeToFun.{0, 0, u1, 0} NNReal NNReal (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal NNReal.semiring NNReal.semiring (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring) (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Λ f))
 but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) {K : TopologicalSpace.Compacts.{u1} X _inst_1} {f : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal}, (forall (x : X), (Membership.mem.{u1, u1} X (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.instMembership.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} X _inst_1)) x K) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X (fun (_x : X) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : X) => NNReal) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 (UniformSpace.toTopologicalSpace.{0} NNReal (PseudoMetricSpace.toUniformSpace.{0} NNReal instPseudoMetricSpaceNNReal)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 instPseudoMetricSpaceNNReal (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal))) f x))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (rieszContentAux.{u1} X _inst_1 Λ K) (FunLike.coe.{succ u1, succ u1, 1} (LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) (fun (_x : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, 0} NNReal NNReal (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal instNNRealSemiring instNNRealSemiring (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring) (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Λ f))
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) {K : TopologicalSpace.Compacts.{u1} X _inst_1} {f : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal}, (forall (x : X), (Membership.mem.{u1, u1} X (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.instMembership.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} X _inst_1)) x K) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X (fun (_x : X) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : X) => NNReal) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 (UniformSpace.toTopologicalSpace.{0} NNReal (PseudoMetricSpace.toUniformSpace.{0} NNReal instPseudoMetricSpaceNNReal)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 instPseudoMetricSpaceNNReal (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal))) f x))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (rieszContentAux.{u1} X _inst_1 Λ K) (FunLike.coe.{succ u1, succ u1, 1} (LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) (fun (_x : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, 0} NNReal NNReal (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal instNNRealSemiring instNNRealSemiring (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring) (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Λ f))
 Case conversion may be inaccurate. Consider using '#align riesz_content_aux_le rieszContentAux_leₓ'. -/
 /-- Any bounded continuous nonnegative f such that `f ≥ 1` on K gives an upper bound on the
 content of K; namely `λ(K) ≤ Λ f`. -/
@@ -111,7 +111,7 @@ theorem rieszContentAux_le {K : Compacts X} {f : X →ᵇ ℝ≥0} (h : ∀ x 
 lean 3 declaration is
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) (K : TopologicalSpace.Compacts.{u1} X _inst_1) {ε : NNReal}, (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) ε) -> (Exists.{succ u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (f : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) => And (forall (x : X), (Membership.Mem.{u1, u1} X (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.hasMem.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.setLike.{u1} X _inst_1)) x K) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) => X -> NNReal) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) f x))) (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (coeFn.{succ u1, succ u1} (LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) (fun (_x : LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) => (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) -> NNReal) (LinearMap.hasCoeToFun.{0, 0, u1, 0} NNReal NNReal (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal NNReal.semiring NNReal.semiring (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring) (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Λ f) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (rieszContentAux.{u1} X _inst_1 Λ K) ε))))
 but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) (K : TopologicalSpace.Compacts.{u1} X _inst_1) {ε : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) ε) -> (Exists.{succ u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) (fun (f : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => And (forall (x : X), (Membership.mem.{u1, u1} X (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.instMembership.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} X _inst_1)) x K) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X (fun (_x : X) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : X) => NNReal) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 (UniformSpace.toTopologicalSpace.{0} NNReal (PseudoMetricSpace.toUniformSpace.{0} NNReal instPseudoMetricSpaceNNReal)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 instPseudoMetricSpaceNNReal (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal))) f x))) (LT.lt.{0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) f) (Preorder.toLT.{0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) f) (PartialOrder.toPreorder.{0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) f) (StrictOrderedSemiring.toPartialOrder.{0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) f) instNNRealStrictOrderedSemiring))) (FunLike.coe.{succ u1, succ u1, 1} (LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) (fun (_x : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, 0} NNReal NNReal (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal instNNRealSemiring instNNRealSemiring (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring) (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Λ f) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) (rieszContentAux.{u1} X _inst_1 Λ K) ε))))
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) (K : TopologicalSpace.Compacts.{u1} X _inst_1) {ε : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) ε) -> (Exists.{succ u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) (fun (f : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => And (forall (x : X), (Membership.mem.{u1, u1} X (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.instMembership.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} X _inst_1)) x K) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X (fun (_x : X) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : X) => NNReal) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 (UniformSpace.toTopologicalSpace.{0} NNReal (PseudoMetricSpace.toUniformSpace.{0} NNReal instPseudoMetricSpaceNNReal)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 instPseudoMetricSpaceNNReal (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal))) f x))) (LT.lt.{0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) f) (Preorder.toLT.{0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) f) (PartialOrder.toPreorder.{0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) f) (StrictOrderedSemiring.toPartialOrder.{0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) f) instNNRealStrictOrderedSemiring))) (FunLike.coe.{succ u1, succ u1, 1} (LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) (fun (_x : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, 0} NNReal NNReal (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal instNNRealSemiring instNNRealSemiring (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring) (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Λ f) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) (rieszContentAux.{u1} X _inst_1 Λ K) ε))))
 Case conversion may be inaccurate. Consider using '#align exists_lt_riesz_content_aux_add_pos exists_lt_rieszContentAux_add_posₓ'. -/
 /-- The Riesz content can be approximated arbitrarily well by evaluating the positive linear
 functional on test functions: for any `ε > 0`, there exists a bounded continuous nonnegative

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jesse Reimann, Kalle Kytölä
 
 ! This file was ported from Lean 3 source module measure_theory.integral.riesz_markov_kakutani
-! leanprover-community/mathlib commit b2ff9a3d7a15fd5b0f060b135421d6a89a999c2f
+! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Topology.Sets.Compacts
 /-!
 #  Riesz–Markov–Kakutani representation theorem
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file will prove different versions of the Riesz-Markov-Kakutani representation theorem.
 The theorem is first proven for compact spaces, from which the statements about linear functionals
 on bounded continuous functions or compactly supported functions on locally compact spaces follow.

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

@@ -41,6 +41,12 @@ variable (Λ : (X →ᵇ ℝ≥0) →ₗ[ℝ≥0] ℝ≥0)
 /-! ### Construction of the content: -/
 
 
+/- warning: riesz_content_aux -> rieszContentAux is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X], (LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) -> (TopologicalSpace.Compacts.{u1} X _inst_1) -> NNReal
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X], (LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) -> (TopologicalSpace.Compacts.{u1} X _inst_1) -> NNReal
+Case conversion may be inaccurate. Consider using '#align riesz_content_aux rieszContentAuxₓ'. -/
 /-- Given a positive linear functional Λ on X, for `K ⊆ X` compact define
 `λ(K) = inf {Λf | 1≤f on K}`. When X is a compact Hausdorff space, this will be shown to be a
 content, and will be shown to agree with the Riesz measure on the compact subsets `K ⊆ X`. -/
@@ -50,6 +56,12 @@ def rieszContentAux : Compacts X → ℝ≥0 := fun K =>
 
 section RieszMonotone
 
+/- warning: riesz_content_aux_image_nonempty -> riesz_content_aux_image_nonempty is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) (K : TopologicalSpace.Compacts.{u1} X _inst_1), Set.Nonempty.{0} NNReal (Set.image.{u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (coeFn.{succ u1, succ u1} (LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) (fun (_x : LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) => (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) -> NNReal) (LinearMap.hasCoeToFun.{0, 0, u1, 0} NNReal NNReal (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal NNReal.semiring NNReal.semiring (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring) (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Λ) (setOf.{u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (f : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) => forall (x : X), (Membership.Mem.{u1, u1} X (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.hasMem.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.setLike.{u1} X _inst_1)) x K) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) => X -> NNReal) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) f x)))))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) (K : TopologicalSpace.Compacts.{u1} X _inst_1), Set.Nonempty.{0} NNReal (Set.image.{u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (FunLike.coe.{succ u1, succ u1, 1} (LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) (fun (_x : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, 0} NNReal NNReal (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal instNNRealSemiring instNNRealSemiring (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring) (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Λ) (setOf.{u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) (fun (f : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => forall (x : X), (Membership.mem.{u1, u1} X (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.instMembership.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} X _inst_1)) x K) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X (fun (_x : X) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : X) => NNReal) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 (UniformSpace.toTopologicalSpace.{0} NNReal (PseudoMetricSpace.toUniformSpace.{0} NNReal instPseudoMetricSpaceNNReal)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 instPseudoMetricSpaceNNReal (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal))) f x)))))
+Case conversion may be inaccurate. Consider using '#align riesz_content_aux_image_nonempty riesz_content_aux_image_nonemptyₓ'. -/
 /-- For any compact subset `K ⊆ X`, there exist some bounded continuous nonnegative
 functions f on X such that `f ≥ 1` on K. -/
 theorem riesz_content_aux_image_nonempty (K : Compacts X) :
@@ -61,6 +73,12 @@ theorem riesz_content_aux_image_nonempty (K : Compacts X) :
   simp only [BoundedContinuousFunction.coe_one, Pi.one_apply]
 #align riesz_content_aux_image_nonempty riesz_content_aux_image_nonempty
 
+/- warning: riesz_content_aux_mono -> rieszContentAux_mono is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) {K₁ : TopologicalSpace.Compacts.{u1} X _inst_1} {K₂ : TopologicalSpace.Compacts.{u1} X _inst_1}, (LE.le.{u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Preorder.toHasLe.{u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.setLike.{u1} X _inst_1)))) K₁ K₂) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (rieszContentAux.{u1} X _inst_1 Λ K₁) (rieszContentAux.{u1} X _inst_1 Λ K₂))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) {K₁ : TopologicalSpace.Compacts.{u1} X _inst_1} {K₂ : TopologicalSpace.Compacts.{u1} X _inst_1}, (LE.le.{u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (Preorder.toLE.{u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (SemilatticeSup.toPartialOrder.{u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (TopologicalSpace.Compacts.instSemilatticeSupCompacts.{u1} X _inst_1)))) K₁ K₂) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (rieszContentAux.{u1} X _inst_1 Λ K₁) (rieszContentAux.{u1} X _inst_1 Λ K₂))
+Case conversion may be inaccurate. Consider using '#align riesz_content_aux_mono rieszContentAux_monoₓ'. -/
 /-- Riesz content λ (associated with a positive linear functional Λ) is
 monotone: if `K₁ ⊆ K₂` are compact subsets in X, then `λ(K₁) ≤ λ(K₂)`. -/
 theorem rieszContentAux_mono {K₁ K₂ : Compacts X} (h : K₁ ≤ K₂) :
@@ -73,6 +91,12 @@ end RieszMonotone
 
 section RieszSubadditive
 
+/- warning: riesz_content_aux_le -> rieszContentAux_le is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) {K : TopologicalSpace.Compacts.{u1} X _inst_1} {f : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace}, (forall (x : X), (Membership.Mem.{u1, u1} X (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.hasMem.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.setLike.{u1} X _inst_1)) x K) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) => X -> NNReal) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) f x))) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (rieszContentAux.{u1} X _inst_1 Λ K) (coeFn.{succ u1, succ u1} (LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) (fun (_x : LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) => (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) -> NNReal) (LinearMap.hasCoeToFun.{0, 0, u1, 0} NNReal NNReal (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal NNReal.semiring NNReal.semiring (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring) (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Λ f))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) {K : TopologicalSpace.Compacts.{u1} X _inst_1} {f : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal}, (forall (x : X), (Membership.mem.{u1, u1} X (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.instMembership.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} X _inst_1)) x K) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X (fun (_x : X) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : X) => NNReal) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 (UniformSpace.toTopologicalSpace.{0} NNReal (PseudoMetricSpace.toUniformSpace.{0} NNReal instPseudoMetricSpaceNNReal)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 instPseudoMetricSpaceNNReal (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal))) f x))) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (rieszContentAux.{u1} X _inst_1 Λ K) (FunLike.coe.{succ u1, succ u1, 1} (LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) (fun (_x : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, 0} NNReal NNReal (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal instNNRealSemiring instNNRealSemiring (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring) (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Λ f))
+Case conversion may be inaccurate. Consider using '#align riesz_content_aux_le rieszContentAux_leₓ'. -/
 /-- Any bounded continuous nonnegative f such that `f ≥ 1` on K gives an upper bound on the
 content of K; namely `λ(K) ≤ Λ f`. -/
 theorem rieszContentAux_le {K : Compacts X} {f : X →ᵇ ℝ≥0} (h : ∀ x ∈ K, (1 : ℝ≥0) ≤ f x) :
@@ -80,6 +104,12 @@ theorem rieszContentAux_le {K : Compacts X} {f : X →ᵇ ℝ≥0} (h : ∀ x 
   csInf_le (OrderBot.bddBelow _) ⟨f, ⟨h, rfl⟩⟩
 #align riesz_content_aux_le rieszContentAux_le
 
+/- warning: exists_lt_riesz_content_aux_add_pos -> exists_lt_rieszContentAux_add_pos is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) (K : TopologicalSpace.Compacts.{u1} X _inst_1) {ε : NNReal}, (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) ε) -> (Exists.{succ u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (f : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) => And (forall (x : X), (Membership.Mem.{u1, u1} X (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.hasMem.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.setLike.{u1} X _inst_1)) x K) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (coeFn.{succ u1, succ u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) (fun (_x : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) => X -> NNReal) (BoundedContinuousFunction.hasCoeToFun.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) f x))) (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (coeFn.{succ u1, succ u1} (LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) (fun (_x : LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) => (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) -> NNReal) (LinearMap.hasCoeToFun.{0, 0, u1, 0} NNReal NNReal (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal NNReal.semiring NNReal.semiring (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring) (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) Λ f) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (rieszContentAux.{u1} X _inst_1 Λ K) ε))))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) (K : TopologicalSpace.Compacts.{u1} X _inst_1) {ε : NNReal}, (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) ε) -> (Exists.{succ u1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) (fun (f : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => And (forall (x : X), (Membership.mem.{u1, u1} X (TopologicalSpace.Compacts.{u1} X _inst_1) (SetLike.instMembership.{u1, u1} (TopologicalSpace.Compacts.{u1} X _inst_1) X (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} X _inst_1)) x K) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (FunLike.coe.{succ u1, succ u1, 1} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X (fun (_x : X) => (fun (a._@.Mathlib.Topology.ContinuousFunction.Bounded._hyg.904 : X) => NNReal) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 (UniformSpace.toTopologicalSpace.{0} NNReal (PseudoMetricSpace.toUniformSpace.{0} NNReal instPseudoMetricSpaceNNReal)) (BoundedContinuousMapClass.toContinuousMapClass.{u1, u1, 0} (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) X NNReal _inst_1 instPseudoMetricSpaceNNReal (BoundedContinuousFunction.instBoundedContinuousMapClassBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal))) f x))) (LT.lt.{0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) f) (Preorder.toLT.{0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) f) (PartialOrder.toPreorder.{0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) f) (StrictOrderedSemiring.toPartialOrder.{0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) f) instNNRealStrictOrderedSemiring))) (FunLike.coe.{succ u1, succ u1, 1} (LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) (fun (_x : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) => NNReal) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, 0} NNReal NNReal (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal instNNRealSemiring instNNRealSemiring (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring) (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) Λ f) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) (rieszContentAux.{u1} X _inst_1 Λ K) ε))))
+Case conversion may be inaccurate. Consider using '#align exists_lt_riesz_content_aux_add_pos exists_lt_rieszContentAux_add_posₓ'. -/
 /-- The Riesz content can be approximated arbitrarily well by evaluating the positive linear
 functional on test functions: for any `ε > 0`, there exists a bounded continuous nonnegative
 function f on X such that `f ≥ 1` on K and such that `λ(K) ≤ Λ f < λ(K) + ε`. -/
@@ -95,6 +125,12 @@ theorem exists_lt_rieszContentAux_add_pos (K : Compacts X) {ε : ℝ≥0} (εpos
   exact α_hyp
 #align exists_lt_riesz_content_aux_add_pos exists_lt_rieszContentAux_add_pos
 
+/- warning: riesz_content_aux_sup_le -> rieszContentAux_sup_le is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal NNReal.semiring NNReal.semiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace) NNReal (BoundedContinuousFunction.addAddCommMonoid.{u1, 0} X NNReal _inst_1 NNReal.pseudoMetricSpace (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal NNReal.pseudoMetricSpace _inst_1 NNReal.pseudoMetricSpace NNReal.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))) (Semiring.toModule.{0} NNReal NNReal.semiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal NNReal.semiring)) (K1 : TopologicalSpace.Compacts.{u1} X _inst_1) (K2 : TopologicalSpace.Compacts.{u1} X _inst_1), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (rieszContentAux.{u1} X _inst_1 Λ (Sup.sup.{u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (TopologicalSpace.Compacts.hasSup.{u1} X _inst_1) K1 K2)) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toHasAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))) (rieszContentAux.{u1} X _inst_1 Λ K1) (rieszContentAux.{u1} X _inst_1 Λ K2))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (Λ : LinearMap.{0, 0, u1, 0} NNReal NNReal instNNRealSemiring instNNRealSemiring (RingHom.id.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring)) (BoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal) NNReal (BoundedContinuousFunction.instAddAddCommMonoidBoundedContinuousFunction.{u1, 0} X NNReal _inst_1 instPseudoMetricSpaceNNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) NNReal.hasLipschitzAdd) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (BoundedContinuousFunction.module.{u1, 0, 0} X NNReal NNReal instPseudoMetricSpaceNNReal _inst_1 instPseudoMetricSpaceNNReal instNNRealSemiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))) (Semiring.toModule.{0} NNReal instNNRealSemiring) NNReal.boundedSMul NNReal.hasLipschitzAdd) (Semiring.toModule.{0} NNReal instNNRealSemiring)) (K1 : TopologicalSpace.Compacts.{u1} X _inst_1) (K2 : TopologicalSpace.Compacts.{u1} X _inst_1), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (rieszContentAux.{u1} X _inst_1 Λ (Sup.sup.{u1} (TopologicalSpace.Compacts.{u1} X _inst_1) (TopologicalSpace.Compacts.instSupCompacts.{u1} X _inst_1) K1 K2)) (HAdd.hAdd.{0, 0, 0} NNReal NNReal NNReal (instHAdd.{0} NNReal (Distrib.toAdd.{0} NNReal (NonUnitalNonAssocSemiring.toDistrib.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal instNNRealSemiring))))) (rieszContentAux.{u1} X _inst_1 Λ K1) (rieszContentAux.{u1} X _inst_1 Λ K2))
+Case conversion may be inaccurate. Consider using '#align riesz_content_aux_sup_le rieszContentAux_sup_leₓ'. -/
 /-- The Riesz content λ associated to a given positive linear functional Λ is
 finitely subadditive: `λ(K₁ ∪ K₂) ≤ λ(K₁) + λ(K₂)` for any compact subsets `K₁, K₂ ⊆ X`. -/
 theorem rieszContentAux_sup_le (K1 K2 : Compacts X) :

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

@@ -45,7 +45,7 @@ variable (Λ : (X →ᵇ ℝ≥0) →ₗ[ℝ≥0] ℝ≥0)
 `λ(K) = inf {Λf | 1≤f on K}`. When X is a compact Hausdorff space, this will be shown to be a
 content, and will be shown to agree with the Riesz measure on the compact subsets `K ⊆ X`. -/
 def rieszContentAux : Compacts X → ℝ≥0 := fun K =>
-  infₛ (Λ '' { f : X →ᵇ ℝ≥0 | ∀ x ∈ K, (1 : ℝ≥0) ≤ f x })
+  sInf (Λ '' { f : X →ᵇ ℝ≥0 | ∀ x ∈ K, (1 : ℝ≥0) ≤ f x })
 #align riesz_content_aux rieszContentAux
 
 section RieszMonotone
@@ -65,7 +65,7 @@ theorem riesz_content_aux_image_nonempty (K : Compacts X) :
 monotone: if `K₁ ⊆ K₂` are compact subsets in X, then `λ(K₁) ≤ λ(K₂)`. -/
 theorem rieszContentAux_mono {K₁ K₂ : Compacts X} (h : K₁ ≤ K₂) :
     rieszContentAux Λ K₁ ≤ rieszContentAux Λ K₂ :=
-  cinfₛ_le_cinfₛ (OrderBot.bddBelow _) (riesz_content_aux_image_nonempty Λ K₂)
+  csInf_le_csInf (OrderBot.bddBelow _) (riesz_content_aux_image_nonempty Λ K₂)
     (image_subset Λ (setOf_subset_setOf.mpr fun f f_hyp x x_in_K₁ => f_hyp x (h x_in_K₁)))
 #align riesz_content_aux_mono rieszContentAux_mono
 
@@ -77,7 +77,7 @@ section RieszSubadditive
 content of K; namely `λ(K) ≤ Λ f`. -/
 theorem rieszContentAux_le {K : Compacts X} {f : X →ᵇ ℝ≥0} (h : ∀ x ∈ K, (1 : ℝ≥0) ≤ f x) :
     rieszContentAux Λ K ≤ Λ f :=
-  cinfₛ_le (OrderBot.bddBelow _) ⟨f, ⟨h, rfl⟩⟩
+  csInf_le (OrderBot.bddBelow _) ⟨f, ⟨h, rfl⟩⟩
 #align riesz_content_aux_le rieszContentAux_le
 
 /-- The Riesz content can be approximated arbitrarily well by evaluating the positive linear
@@ -88,7 +88,7 @@ theorem exists_lt_rieszContentAux_add_pos (K : Compacts X) {ε : ℝ≥0} (εpos
   by
   --choose a test function `f` s.t. `Λf = α < λ(K) + ε`
   obtain ⟨α, ⟨⟨f, f_hyp⟩, α_hyp⟩⟩ :=
-    exists_lt_of_cinfₛ_lt (riesz_content_aux_image_nonempty Λ K)
+    exists_lt_of_csInf_lt (riesz_content_aux_image_nonempty Λ K)
       (lt_add_of_pos_right (rieszContentAux Λ K) εpos)
   refine' ⟨f, f_hyp.left, _⟩
   rw [f_hyp.right]

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

@@ -30,7 +30,7 @@ compact subsets of the space X, rather than the usual construction of open sets
 
 noncomputable section
 
-open BoundedContinuousFunction NNReal Ennreal
+open BoundedContinuousFunction NNReal ENNReal
 
 open Set Function TopologicalSpace
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/271bf175e6c51b8d31d6c0107b7bb4a967c7277e

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jesse Reimann, Kalle Kytölä
 
 ! This file was ported from Lean 3 source module measure_theory.integral.riesz_markov_kakutani
-! leanprover-community/mathlib commit 717c073262cd9d59b1a1dcda7e8ab570c5b63370
+! leanprover-community/mathlib commit b2ff9a3d7a15fd5b0f060b135421d6a89a999c2f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -103,8 +103,8 @@ theorem rieszContentAux_sup_le (K1 K2 : Compacts X) :
   apply NNReal.le_of_forall_pos_le_add
   intro ε εpos
   --get test functions s.t. `λ(Ki) ≤ Λfi ≤ λ(Ki) + ε/2, i=1,2`
-  obtain ⟨f1, f_test_function_K1⟩ := exists_lt_rieszContentAux_add_pos Λ K1 (NNReal.half_pos εpos)
-  obtain ⟨f2, f_test_function_K2⟩ := exists_lt_rieszContentAux_add_pos Λ K2 (NNReal.half_pos εpos)
+  obtain ⟨f1, f_test_function_K1⟩ := exists_lt_rieszContentAux_add_pos Λ K1 (half_pos εpos)
+  obtain ⟨f2, f_test_function_K2⟩ := exists_lt_rieszContentAux_add_pos Λ K2 (half_pos εpos)
   --let `f := f1 + f2` test function for the content of `K`
   have f_test_function_union : ∀ x ∈ K1 ⊔ K2, (1 : ℝ≥0) ≤ (f1 + f2) x :=
     by
@@ -116,7 +116,7 @@ theorem rieszContentAux_sup_le (K1 K2 : Compacts X) :
   rw [map_add]
   --use that `Λfi` are lower bounds for `λ(Ki) + ε/2`
   apply lt_of_lt_of_le (add_lt_add f_test_function_K1.right f_test_function_K2.right) (le_of_eq _)
-  rw [add_assoc, add_comm (ε / 2), add_assoc, NNReal.add_halves ε, add_assoc]
+  rw [add_assoc, add_comm (ε / 2), add_assoc, add_halves ε, add_assoc]
 #align riesz_content_aux_sup_le rieszContentAux_sup_le
 
 end RieszSubadditive

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

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)

@@ -32,7 +32,6 @@ open BoundedContinuousFunction NNReal ENNReal
 open Set Function TopologicalSpace
 
 variable {X : Type*} [TopologicalSpace X]
-
 variable (Λ : (X →ᵇ ℝ≥0) →ₗ[ℝ≥0] ℝ≥0)
 
 /-! ### Construction of the content: -/

• rename Finset.Nonempty.image_iff to Finset.image_nonempty, deprecate the old version;
• rename Set.nonempty_image_iff to Set.image_nonempty, deprecate the old version;
• drop unneeded Finset.Nonempty arguments here and there;
• add versions of some lemmas that assume Nonempty s instead of Nonempty (s.image f) or Nonempty (s.map f).

@@ -51,7 +51,7 @@ section RieszMonotone
 functions f on X such that `f ≥ 1` on K. -/
 theorem rieszContentAux_image_nonempty (K : Compacts X) :
     (Λ '' { f : X →ᵇ ℝ≥0 | ∀ x ∈ K, (1 : ℝ≥0) ≤ f x }).Nonempty := by
-  rw [nonempty_image_iff]
+  rw [image_nonempty]
   use (1 : X →ᵇ ℝ≥0)
   intro x _
   simp only [BoundedContinuousFunction.coe_one, Pi.one_apply]; rfl

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

This has nice performance benefits.

@@ -31,7 +31,7 @@ open BoundedContinuousFunction NNReal ENNReal
 
 open Set Function TopologicalSpace
 
-variable {X : Type _} [TopologicalSpace X]
+variable {X : Type*} [TopologicalSpace X]
 
 variable (Λ : (X →ᵇ ℝ≥0) →ₗ[ℝ≥0] ℝ≥0)
 

@@ -49,19 +49,19 @@ section RieszMonotone
 
 /-- For any compact subset `K ⊆ X`, there exist some bounded continuous nonnegative
 functions f on X such that `f ≥ 1` on K. -/
-theorem riesz_content_aux_image_nonempty (K : Compacts X) :
+theorem rieszContentAux_image_nonempty (K : Compacts X) :
     (Λ '' { f : X →ᵇ ℝ≥0 | ∀ x ∈ K, (1 : ℝ≥0) ≤ f x }).Nonempty := by
   rw [nonempty_image_iff]
   use (1 : X →ᵇ ℝ≥0)
   intro x _
   simp only [BoundedContinuousFunction.coe_one, Pi.one_apply]; rfl
-#align riesz_content_aux_image_nonempty riesz_content_aux_image_nonempty
+#align riesz_content_aux_image_nonempty rieszContentAux_image_nonempty
 
 /-- Riesz content λ (associated with a positive linear functional Λ) is
 monotone: if `K₁ ⊆ K₂` are compact subsets in X, then `λ(K₁) ≤ λ(K₂)`. -/
 theorem rieszContentAux_mono {K₁ K₂ : Compacts X} (h : K₁ ≤ K₂) :
     rieszContentAux Λ K₁ ≤ rieszContentAux Λ K₂ :=
-  csInf_le_csInf (OrderBot.bddBelow _) (riesz_content_aux_image_nonempty Λ K₂)
+  csInf_le_csInf (OrderBot.bddBelow _) (rieszContentAux_image_nonempty Λ K₂)
     (image_subset Λ (setOf_subset_setOf.mpr fun _ f_hyp x x_in_K₁ => f_hyp x (h x_in_K₁)))
 #align riesz_content_aux_mono rieszContentAux_mono
 
@@ -83,7 +83,7 @@ theorem exists_lt_rieszContentAux_add_pos (K : Compacts X) {ε : ℝ≥0} (εpos
     ∃ f : X →ᵇ ℝ≥0, (∀ x ∈ K, (1 : ℝ≥0) ≤ f x) ∧ Λ f < rieszContentAux Λ K + ε := by
   --choose a test function `f` s.t. `Λf = α < λ(K) + ε`
   obtain ⟨α, ⟨⟨f, f_hyp⟩, α_hyp⟩⟩ :=
-    exists_lt_of_csInf_lt (riesz_content_aux_image_nonempty Λ K)
+    exists_lt_of_csInf_lt (rieszContentAux_image_nonempty Λ K)
       (lt_add_of_pos_right (rieszContentAux Λ K) εpos)
   refine' ⟨f, f_hyp.left, _⟩
   rw [f_hyp.right]

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Jesse Reimann. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jesse Reimann, Kalle Kytölä
-
-! This file was ported from Lean 3 source module measure_theory.integral.riesz_markov_kakutani
-! leanprover-community/mathlib commit b2ff9a3d7a15fd5b0f060b135421d6a89a999c2f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.ContinuousFunction.Bounded
 import Mathlib.Topology.Sets.Compacts
 
+#align_import measure_theory.integral.riesz_markov_kakutani from "leanprover-community/mathlib"@"b2ff9a3d7a15fd5b0f060b135421d6a89a999c2f"
+
 /-!
 #  Riesz–Markov–Kakutani representation theorem