phillips ⟷ Counterexamples.Phillips

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

@@ -402,7 +402,7 @@ theorem continuousPart_apply_eq_zero_of_countable (f : BoundedAdditiveMeasure α
   simp [continuous_part]
   convert f.apply_countable s hs using 2
   ext x
-  simp [and_comm']
+  simp [and_comm]
 #align counterexample.phillips_1940.bounded_additive_measure.continuous_part_apply_eq_zero_of_countable Counterexample.Phillips1940.BoundedAdditiveMeasure.continuousPart_apply_eq_zero_of_countable
 
 theorem continuousPart_apply_diff (f : BoundedAdditiveMeasure α) (s t : Set α) (hs : s.Countable) :

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

@@ -217,8 +217,8 @@ theorem le_bound (f : BoundedAdditiveMeasure α) (s : Set α) : f s ≤ f.C :=
 theorem empty (f : BoundedAdditiveMeasure α) : f ∅ = 0 :=
   by
   have : (∅ : Set α) = ∅ ∪ ∅ := by simp only [empty_union]
-  apply_fun f at this 
-  rwa [f.additive _ _ (empty_disjoint _), self_eq_add_left] at this 
+  apply_fun f at this
+  rwa [f.additive _ _ (empty_disjoint _), self_eq_add_left] at this
 #align counterexample.phillips_1940.bounded_additive_measure.empty Counterexample.Phillips1940.BoundedAdditiveMeasure.empty
 
 instance : Neg (BoundedAdditiveMeasure α) :=
@@ -350,7 +350,7 @@ theorem exists_discrete_support (f : BoundedAdditiveMeasure α) :
     exact h₁ _ (ht.mono (diff_subset _ _))
   · have : t \ (s₁ ∪ s₂) = (t \ (s₁ ∪ s₂)) \ s₂ := by rw [diff_diff, union_assoc, union_self]
     rw [this]
-    simp only [neg_nonpos, neg_apply] at h₂ 
+    simp only [neg_nonpos, neg_apply] at h₂
     exact h₂ _ (ht.mono (diff_subset _ _))
 #align counterexample.phillips_1940.bounded_additive_measure.exists_discrete_support Counterexample.Phillips1940.BoundedAdditiveMeasure.exists_discrete_support
 
@@ -593,15 +593,15 @@ theorem countable_ne (Hcont : (#ℝ) = aleph 1) (φ : (DiscreteCopy ℝ →ᵇ 
     by
     intro x hx
     contrapose! hx
-    simp only [Classical.not_not, mem_set_of_eq] at hx 
+    simp only [Classical.not_not, mem_set_of_eq] at hx
     simp [apply_f_eq_continuous_part Hcont φ x hx]
   have B :
     {x | φ.to_bounded_additive_measure.discrete_support ∩ spf Hcont x ≠ ∅} ⊆
       ⋃ y ∈ φ.to_bounded_additive_measure.discrete_support, {x | y ∈ spf Hcont x} :=
     by
     intro x hx
-    dsimp at hx 
-    rw [← Ne.def, ← nonempty_iff_ne_empty] at hx 
+    dsimp at hx
+    rw [← Ne.def, ← nonempty_iff_ne_empty] at hx
     simp only [exists_prop, mem_Union, mem_set_of_eq]
     exact hx
   apply countable.mono (subset.trans A B)
@@ -664,15 +664,15 @@ theorem no_pettis_integral (Hcont : (#ℝ) = aleph 1) :
         ∀ φ : (DiscreteCopy ℝ →ᵇ ℝ) →L[ℝ] ℝ, ∫ x in Icc 0 1, φ (f Hcont x) = φ g :=
   by
   rintro ⟨g, h⟩
-  simp only [integral_comp] at h 
+  simp only [integral_comp] at h
   have : g = 0 := by
     ext x
     have : g x = eval_clm ℝ x g := rfl
     rw [this, ← h]
     simp
-  simp only [this, ContinuousLinearMap.map_zero] at h 
+  simp only [this, ContinuousLinearMap.map_zero] at h
   specialize h (volume.restrict (Icc (0 : ℝ) 1)).extensionToBoundedFunctions
-  simp_rw [to_functions_to_measure_continuous_part _ _ MeasurableSet.univ] at h 
+  simp_rw [to_functions_to_measure_continuous_part _ _ MeasurableSet.univ] at h
   simpa using h
 #align counterexample.phillips_1940.no_pettis_integral Counterexample.Phillips1940.no_pettis_integral
 

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

@@ -454,16 +454,16 @@ def ContinuousLinearMap.toBoundedAdditiveMeasure [TopologicalSpace α] [Discrete
 #align continuous_linear_map.to_bounded_additive_measure ContinuousLinearMap.toBoundedAdditiveMeasure
 
 @[simp]
-theorem continuousPart_evalClm_eq_zero [TopologicalSpace α] [DiscreteTopology α] (s : Set α)
-    (x : α) : (evalClm ℝ x).toBoundedAdditiveMeasure.continuousPart s = 0 :=
-  let f := (evalClm ℝ x).toBoundedAdditiveMeasure
+theorem continuousPart_evalCLM_eq_zero [TopologicalSpace α] [DiscreteTopology α] (s : Set α)
+    (x : α) : (evalCLM ℝ x).toBoundedAdditiveMeasure.continuousPart s = 0 :=
+  let f := (evalCLM ℝ x).toBoundedAdditiveMeasure
   calc
     f.continuousPart s = f.continuousPart (s \ {x}) :=
       (continuousPart_apply_diff _ _ _ (countable_singleton x)).symm
     _ = f (univ \ f.discreteSupport ∩ (s \ {x})) := rfl
     _ = indicator (univ \ f.discreteSupport ∩ (s \ {x})) 1 x := rfl
     _ = 0 := by simp
-#align counterexample.phillips_1940.continuous_part_eval_clm_eq_zero Counterexample.Phillips1940.continuousPart_evalClm_eq_zero
+#align counterexample.phillips_1940.continuous_part_eval_clm_eq_zero Counterexample.Phillips1940.continuousPart_evalCLM_eq_zero
 
 theorem to_functions_to_measure [MeasurableSpace α] (μ : Measure α) [IsFiniteMeasure μ] (s : Set α)
     (hs : MeasurableSet s) :

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

@@ -266,7 +266,7 @@ theorem exists_discrete_support_nonpos (f : BoundedAdditiveMeasure α) :
     In this proof, we use explicit coercions `↑s` for `s : A` as otherwise the system tries to find
     a `has_coe_to_fun` instance on `↥A`, which is too costly.
     -/
-  by_contra' h
+  by_contra! h
   -- We will formulate things in terms of the type of countable subsets of `α`, as this is more
   -- convenient to formalize the inductive construction.
   let A : Set (Set α) := {t | t.Countable}

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

@@ -3,10 +3,10 @@ Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
-import Mathbin.Analysis.NormedSpace.HahnBanach.Extension
-import Mathbin.MeasureTheory.Integral.SetIntegral
-import Mathbin.MeasureTheory.Measure.Lebesgue.Basic
-import Mathbin.Topology.ContinuousFunction.Bounded
+import Analysis.NormedSpace.HahnBanach.Extension
+import MeasureTheory.Integral.SetIntegral
+import MeasureTheory.Measure.Lebesgue.Basic
+import Topology.ContinuousFunction.Bounded
 
 #align_import phillips from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
 

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module phillips
-! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.NormedSpace.HahnBanach.Extension
 import Mathbin.MeasureTheory.Integral.SetIntegral
 import Mathbin.MeasureTheory.Measure.Lebesgue.Basic
 import Mathbin.Topology.ContinuousFunction.Bounded
 
+#align_import phillips from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
+
 /-!
 # A counterexample on Pettis integrability
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/bf2428c9486c407ca38b5b3fb10b87dad0bc99fa

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module phillips
-! leanprover-community/mathlib commit 328375597f2c0dd00522d9c2e5a33b6a6128feeb
+! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Topology.ContinuousFunction.Bounded
 /-!
 # A counterexample on Pettis integrability
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 There are several theories of integration for functions taking values in Banach spaces. Bochner
 integration, requiring approximation by simple functions, is the analogue of the one-dimensional
 theory. It is very well behaved, but only works for functions with second-countable range.

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -474,7 +474,7 @@ theorem to_functions_to_measure [MeasurableSpace α] (μ : Measure α) [IsFinite
         (of_normed_add_comm_group_discrete (indicator s 1) 1 (norm_indicator_le_one s)) =
       (μ s).toReal
   rw [extension_to_bounded_functions_apply]
-  · change (∫ x, s.indicator (fun y => (1 : ℝ)) x ∂μ) = _
+  · change ∫ x, s.indicator (fun y => (1 : ℝ)) x ∂μ = _
     simp [integral_indicator hs]
   · change integrable (indicator s 1) μ
     have : integrable (fun x => (1 : ℝ)) μ := integrable_const (1 : ℝ)
@@ -629,7 +629,7 @@ theorem integrable_comp (Hcont : (#ℝ) = aleph 1) (φ : (DiscreteCopy ℝ →
 #align counterexample.phillips_1940.integrable_comp Counterexample.Phillips1940.integrable_comp
 
 theorem integral_comp (Hcont : (#ℝ) = aleph 1) (φ : (DiscreteCopy ℝ →ᵇ ℝ) →L[ℝ] ℝ) :
-    (∫ x in Icc 0 1, φ (f Hcont x)) = φ.toBoundedAdditiveMeasure.continuousPart univ :=
+    ∫ x in Icc 0 1, φ (f Hcont x) = φ.toBoundedAdditiveMeasure.continuousPart univ :=
   by
   rw [← integral_congr_ae (comp_ae_eq_const Hcont φ)]
   simp
@@ -661,7 +661,7 @@ theorem norm_bound (Hcont : (#ℝ) = aleph 1) (x : ℝ) : ‖f Hcont x‖ ≤ 1
 /-- The function `f Hcont : ℝ → (discrete_copy ℝ →ᵇ ℝ)` has no Pettis integral. -/
 theorem no_pettis_integral (Hcont : (#ℝ) = aleph 1) :
     ¬∃ g : DiscreteCopy ℝ →ᵇ ℝ,
-        ∀ φ : (DiscreteCopy ℝ →ᵇ ℝ) →L[ℝ] ℝ, (∫ x in Icc 0 1, φ (f Hcont x)) = φ g :=
+        ∀ φ : (DiscreteCopy ℝ →ᵇ ℝ) →L[ℝ] ℝ, ∫ x in Icc 0 1, φ (f Hcont x) = φ g :=
   by
   rintro ⟨g, h⟩
   simp only [integral_comp] at h 

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

@@ -296,7 +296,6 @@ theorem exists_discrete_support_nonpos (f : BoundedAdditiveMeasure α) :
       f (↑u \ ↑s) ≤ S := le_ciSup B _
       _ = 2 * (S / 2) := by ring
       _ ≤ 2 * f (↑t \ ↑s) := mul_le_mul_of_nonneg_left ht.le (by norm_num)
-      
   choose! F hF using this
   -- iterate the above construction, by adding at each step a set with measure close to maximal in
   -- the complement of already chosen points. This is the set `s n` at step `n`.
@@ -333,7 +332,6 @@ theorem exists_discrete_support_nonpos (f : BoundedAdditiveMeasure α) :
       calc
         ((n + 1 : ℕ) : ℝ) * (ε / 2) = ε / 2 + n * (ε / 2) := by simp only [Nat.cast_succ] <;> ring
         _ ≤ f (↑(s (n + 1 : ℕ)) \ ↑(s n)) + f ↑(s n) := add_le_add (I1 n) IH
-        
   rcases exists_nat_gt (f.C / (ε / 2)) with ⟨n, hn⟩
   have : (n : ℝ) ≤ f.C / (ε / 2) := by rw [le_div_iff (half_pos ε_pos)];
     exact (I2 n).trans (f.le_bound _)
@@ -465,7 +463,6 @@ theorem continuousPart_evalClm_eq_zero [TopologicalSpace α] [DiscreteTopology 
     _ = f (univ \ f.discreteSupport ∩ (s \ {x})) := rfl
     _ = indicator (univ \ f.discreteSupport ∩ (s \ {x})) 1 x := rfl
     _ = 0 := by simp
-    
 #align counterexample.phillips_1940.continuous_part_eval_clm_eq_zero Counterexample.Phillips1940.continuousPart_evalClm_eq_zero
 
 theorem to_functions_to_measure [MeasurableSpace α] (μ : Measure α) [IsFiniteMeasure μ] (s : Set α)

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090

@@ -577,7 +577,7 @@ theorem countable_ne (Hcont : #ℝ = aleph 1) (φ : (DiscreteCopy ℝ →ᵇ ℝ
       ⋃ y ∈ φ.toBoundedAdditiveMeasure.discreteSupport, {x | y ∈ spf Hcont x} := by
     intro x hx
     dsimp at hx
-    rw [← Ne.def, ← nonempty_iff_ne_empty] at hx
+    rw [← Ne, ← nonempty_iff_ne_empty] at hx
     simp only [exists_prop, mem_iUnion, mem_setOf_eq]
     exact hx
   apply Countable.mono (Subset.trans A B)

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

@@ -312,7 +312,7 @@ theorem exists_discrete_support_nonpos (f : BoundedAdditiveMeasure α) :
   have I2 : ∀ n : ℕ, (n : ℝ) * (ε / 2) ≤ f ↑(s n) := by
     intro n
     induction' n with n IH
-    · simp only [s, BoundedAdditiveMeasure.empty, id.def, Nat.cast_zero, zero_mul,
+    · simp only [s, BoundedAdditiveMeasure.empty, id, Nat.cast_zero, zero_mul,
         Function.iterate_zero, Subtype.coe_mk, Nat.zero_eq]
       rfl
     · have : (s (n + 1)).1 = (s (n + 1)).1 \ (s n).1 ∪ (s n).1 := by

Standardizes the following names for distributivity laws across Finset and Set:

• inter_union_distrib_left
• inter_union_distrib_right
• union_inter_distrib_left
• union_inter_distrib_right

Makes arguments explicit in:

• Set.union_inter_distrib_right
• Set.union_inter_distrib_left
• Set.inter_union_distrib_right

Deprecates these theorem names:

• Finset.inter_distrib_left
• Finset.inter_distrib_right
• Finset.union_distrib_right
• Finset.union_distrib_left
• Set.inter_distrib_left
• Set.inter_distrib_right
• Set.union_distrib_right
• Set.union_distrib_left

Fixes use of deprecated names and implicit arguments in these files:

• Topology/Basic
• Topology/Connected/Basic
• MeasureTheory/MeasurableSpace/Basic
• MeasureTheory/Covering/Differentiation
• MeasureTheory/Constructions/BorelSpace/Basic
• Data/Set/Image
• Data/Set/Basic
• Data/PFun
• Data/Matroid/Dual
• Data/Finset/Sups
• Data/Finset/Basic
• Combinatorics/SetFamily/FourFunctions
• Combinatorics/Additive/SalemSpencer
• Counterexamples/Phillips.lean
• Archive/Imo/Imo2021Q1.lean

@@ -374,7 +374,7 @@ def continuousPart (f : BoundedAdditiveMeasure α) : BoundedAdditiveMeasure α :
 theorem eq_add_parts (f : BoundedAdditiveMeasure α) (s : Set α) :
     f s = f.discretePart s + f.continuousPart s := by
   simp only [discretePart, continuousPart, restrict_apply]
-  rw [← f.additive, ← inter_distrib_right]
+  rw [← f.additive, ← union_inter_distrib_right]
   · simp only [union_univ, union_diff_self, univ_inter]
   · have : Disjoint f.discreteSupport (univ \ f.discreteSupport) := disjoint_sdiff_self_right
     exact this.mono (inter_subset_left _ _) (inter_subset_left _ _)

The termination checker has been getting more capable, and many of the termination_by or decreasing_by clauses in Mathlib are no longer needed.

(Note that termination_by? will show the automatically derived termination expression, so no information is being lost by removing these.)

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

@@ -498,7 +498,6 @@ We need the continuum hypothesis to construct it.
 theorem sierpinski_pathological_family (Hcont : #ℝ = aleph 1) :
     ∃ f : ℝ → Set ℝ, (∀ x, (univ \ f x).Countable) ∧ ∀ y, {x : ℝ | y ∈ f x}.Countable := by
   rcases Cardinal.ord_eq ℝ with ⟨r, hr, H⟩
-  skip
   refine' ⟨fun x => {y | r x y}, fun x => _, fun y => _⟩
   · have : univ \ {y | r x y} = {y | r y x} ∪ {x} := by
       ext y

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

@@ -413,7 +413,8 @@ section
 
 
 theorem norm_indicator_le_one (s : Set α) (x : α) : ‖(indicator s (1 : α → ℝ)) x‖ ≤ 1 := by
-  simp only [indicator, Pi.one_apply]; split_ifs <;> norm_num
+  simp only [indicator, Pi.one_apply]; split_ifs <;>
+  set_option tactic.skipAssignedInstances false in norm_num
 #align counterexample.phillips_1940.norm_indicator_le_one Counterexample.Phillips1940.norm_indicator_le_one
 
 /-- A functional in the dual space of bounded functions gives rise to a bounded additive measure,

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

@@ -308,15 +308,15 @@ theorem exists_discrete_support_nonpos (f : BoundedAdditiveMeasure α) :
       simp only [not_exists, mem_iUnion, mem_diff]
       tauto
     · congr 1
-      simp only [Function.iterate_succ', Subtype.coe_mk, union_diff_left, Function.comp]
+      simp only [s, Function.iterate_succ', Subtype.coe_mk, union_diff_left, Function.comp]
   have I2 : ∀ n : ℕ, (n : ℝ) * (ε / 2) ≤ f ↑(s n) := by
     intro n
     induction' n with n IH
-    · simp only [BoundedAdditiveMeasure.empty, id.def, Nat.cast_zero, zero_mul,
+    · simp only [s, BoundedAdditiveMeasure.empty, id.def, Nat.cast_zero, zero_mul,
         Function.iterate_zero, Subtype.coe_mk, Nat.zero_eq]
       rfl
     · have : (s (n + 1)).1 = (s (n + 1)).1 \ (s n).1 ∪ (s n).1 := by
-        simpa only [Function.iterate_succ', union_diff_self]
+        simpa only [s, Function.iterate_succ', union_diff_self]
           using (diff_union_of_subset <| subset_union_left _ _).symm
       rw [Nat.succ_eq_add_one, this, f.additive]
       swap; · exact disjoint_sdiff_self_left

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

@@ -434,7 +434,7 @@ def _root_.ContinuousLinearMap.toBoundedAdditiveMeasure [TopologicalSpace α] [D
       have I :
         ‖ofNormedAddCommGroupDiscrete (indicator s 1) 1 (norm_indicator_le_one s)‖ ≤ 1 := by
         apply norm_ofNormedAddCommGroup_le _ zero_le_one
-      apply le_trans (f.le_op_norm _)
+      apply le_trans (f.le_opNorm _)
       simpa using mul_le_mul_of_nonneg_left I (norm_nonneg f)⟩
 #align continuous_linear_map.to_bounded_additive_measure ContinuousLinearMap.toBoundedAdditiveMeasure
 

Redefine Set.Countable s as _root_.Countable s. Fix compile, golf some of the broken proofs.

@@ -315,9 +315,9 @@ theorem exists_discrete_support_nonpos (f : BoundedAdditiveMeasure α) :
     · simp only [BoundedAdditiveMeasure.empty, id.def, Nat.cast_zero, zero_mul,
         Function.iterate_zero, Subtype.coe_mk, Nat.zero_eq]
       rfl
-    · have : (↑(s (n + 1)) : Set α) = ↑(s (n + 1)) \ ↑(s n) ∪ ↑(s n) := by
-        simp only [Function.iterate_succ', union_comm, union_diff_self, Subtype.coe_mk,
-          union_diff_left, Function.comp]
+    · have : (s (n + 1)).1 = (s (n + 1)).1 \ (s n).1 ∪ (s n).1 := by
+        simpa only [Function.iterate_succ', union_diff_self]
+          using (diff_union_of_subset <| subset_union_left _ _).symm
       rw [Nat.succ_eq_add_one, this, f.additive]
       swap; · exact disjoint_sdiff_self_left
       calc

Rename

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

and related theorems.

@@ -439,16 +439,16 @@ def _root_.ContinuousLinearMap.toBoundedAdditiveMeasure [TopologicalSpace α] [D
 #align continuous_linear_map.to_bounded_additive_measure ContinuousLinearMap.toBoundedAdditiveMeasure
 
 @[simp]
-theorem continuousPart_evalClm_eq_zero [TopologicalSpace α] [DiscreteTopology α] (s : Set α)
-    (x : α) : (evalClm ℝ x).toBoundedAdditiveMeasure.continuousPart s = 0 :=
-  let f := (evalClm ℝ x).toBoundedAdditiveMeasure
+theorem continuousPart_evalCLM_eq_zero [TopologicalSpace α] [DiscreteTopology α] (s : Set α)
+    (x : α) : (evalCLM ℝ x).toBoundedAdditiveMeasure.continuousPart s = 0 :=
+  let f := (evalCLM ℝ x).toBoundedAdditiveMeasure
   calc
     f.continuousPart s = f.continuousPart (s \ {x}) :=
       (continuousPart_apply_diff _ _ _ (countable_singleton x)).symm
     _ = f (univ \ f.discreteSupport ∩ (s \ {x})) := rfl
     _ = indicator (univ \ f.discreteSupport ∩ (s \ {x})) 1 x := rfl
     _ = 0 := by simp
-#align counterexample.phillips_1940.continuous_part_eval_clm_eq_zero Counterexample.Phillips1940.continuousPart_evalClm_eq_zero
+#align counterexample.phillips_1940.continuous_part_eval_clm_eq_zero Counterexample.Phillips1940.continuousPart_evalCLM_eq_zero
 
 theorem toFunctions_toMeasure [MeasurableSpace α] (μ : Measure α) [IsFiniteMeasure μ] (s : Set α)
     (hs : MeasurableSet s) :
@@ -638,7 +638,7 @@ theorem no_pettis_integral (Hcont : #ℝ = aleph 1) :
   simp only [integral_comp] at h
   have : g = 0 := by
     ext x
-    have : g x = evalClm ℝ x g := rfl
+    have : g x = evalCLM ℝ x g := rfl
     rw [this, ← h]
     simp
   simp only [this, ContinuousLinearMap.map_zero] at h

@@ -287,8 +287,7 @@ theorem exists_discrete_support_nonpos (f : BoundedAdditiveMeasure α) :
     refine' ⟨t, fun u => _⟩
     calc
       f (↑u \ ↑s) ≤ S := le_ciSup B _
-      _ = 2 * (S / 2) := by ring
-      _ ≤ 2 * f (↑t \ ↑s) := mul_le_mul_of_nonneg_left ht.le (by norm_num)
+      _ ≤ 2 * f (↑t \ ↑s) := (div_le_iff' two_pos).1 ht.le
   choose! F hF using this
   -- iterate the above construction, by adding at each step a set with measure close to maximal in
   -- the complement of already chosen points. This is the set `s n` at step `n`.

@@ -570,9 +570,9 @@ theorem countable_ne (Hcont : #ℝ = aleph 1) (φ : (DiscreteCopy ℝ →ᵇ ℝ
     {x | φ.toBoundedAdditiveMeasure.continuousPart univ ≠ φ (f Hcont x)} ⊆
       {x | φ.toBoundedAdditiveMeasure.discreteSupport ∩ spf Hcont x ≠ ∅} := by
     intro x hx
+    simp only [mem_setOf] at *
     contrapose! hx
-    simp only [Classical.not_not, mem_setOf_eq, not_nonempty_iff_eq_empty] at hx
-    simp [apply_f_eq_continuousPart Hcont φ x hx]
+    exact apply_f_eq_continuousPart Hcont φ x hx |>.symm
   have B :
     {x | φ.toBoundedAdditiveMeasure.discreteSupport ∩ spf Hcont x ≠ ∅} ⊆
       ⋃ y ∈ φ.toBoundedAdditiveMeasure.discreteSupport, {x | y ∈ spf Hcont x} := by

To fit with the "please try harder" convention of ! tactics.

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

@@ -261,7 +261,7 @@ theorem exists_discrete_support_nonpos (f : BoundedAdditiveMeasure α) :
     In this proof, we use explicit coercions `↑s` for `s : A` as otherwise the system tries to find
     a `CoeFun` instance on `↥A`, which is too costly.
     -/
-  by_contra' h
+  by_contra! h
   -- We will formulate things in terms of the type of countable subsets of `α`, as this is more
   -- convenient to formalize the inductive construction.
   let A : Set (Set α) := {t | t.Countable}

Co-authored-by: Kyle Miller <kmill31415@gmail.com>

@@ -571,7 +571,7 @@ theorem countable_ne (Hcont : #ℝ = aleph 1) (φ : (DiscreteCopy ℝ →ᵇ ℝ
       {x | φ.toBoundedAdditiveMeasure.discreteSupport ∩ spf Hcont x ≠ ∅} := by
     intro x hx
     contrapose! hx
-    simp only [Classical.not_not, mem_setOf_eq] at hx
+    simp only [Classical.not_not, mem_setOf_eq, not_nonempty_iff_eq_empty] at hx
     simp [apply_f_eq_continuousPart Hcont φ x hx]
   have B :
     {x | φ.toBoundedAdditiveMeasure.discreteSupport ∩ spf Hcont x ≠ ∅} ⊆

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

@@ -333,7 +333,7 @@ theorem exists_discrete_support_nonpos (f : BoundedAdditiveMeasure α) :
 theorem exists_discrete_support (f : BoundedAdditiveMeasure α) :
     ∃ s : Set α, s.Countable ∧ ∀ t : Set α, t.Countable → f (t \ s) = 0 := by
   rcases f.exists_discrete_support_nonpos with ⟨s₁, s₁_count, h₁⟩
-  rcases(-f).exists_discrete_support_nonpos with ⟨s₂, s₂_count, h₂⟩
+  rcases (-f).exists_discrete_support_nonpos with ⟨s₂, s₂_count, h₂⟩
   refine' ⟨s₁ ∪ s₂, s₁_count.union s₂_count, fun t ht => le_antisymm _ _⟩
   · have : t \ (s₁ ∪ s₂) = (t \ (s₁ ∪ s₂)) \ s₁ := by
       rw [diff_diff, union_comm, union_assoc, union_self]

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

@@ -313,7 +313,7 @@ theorem exists_discrete_support_nonpos (f : BoundedAdditiveMeasure α) :
   have I2 : ∀ n : ℕ, (n : ℝ) * (ε / 2) ≤ f ↑(s n) := by
     intro n
     induction' n with n IH
-    · simp only [BoundedAdditiveMeasure.empty, id.def, Nat.cast_zero, MulZeroClass.zero_mul,
+    · simp only [BoundedAdditiveMeasure.empty, id.def, Nat.cast_zero, zero_mul,
         Function.iterate_zero, Subtype.coe_mk, Nat.zero_eq]
       rfl
     · have : (↑(s (n + 1)) : Set α) = ↑(s (n + 1)) \ ↑(s n) ∪ ↑(s n) := by

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module phillips
-! leanprover-community/mathlib commit 328375597f2c0dd00522d9c2e5a33b6a6128feeb
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.NormedSpace.HahnBanach.Extension
 import Mathlib.MeasureTheory.Integral.SetIntegral
 import Mathlib.MeasureTheory.Measure.Lebesgue.Basic
 import Mathlib.Topology.ContinuousFunction.Bounded
 
+#align_import phillips from "leanprover-community/mathlib"@"328375597f2c0dd00522d9c2e5a33b6a6128feeb"
+
 /-!
 # A counterexample on Pettis integrability
 

@@ -498,7 +498,7 @@ We need the continuum hypothesis to construct it.
 -/
 
 
-theorem sierpinski_pathological_family (Hcont : (#ℝ) = aleph 1) :
+theorem sierpinski_pathological_family (Hcont : #ℝ = aleph 1) :
     ∃ f : ℝ → Set ℝ, (∀ x, (univ \ f x).Countable) ∧ ∀ y, {x : ℝ | y ∈ f x}.Countable := by
   rcases Cardinal.ord_eq ℝ with ⟨r, hr, H⟩
   skip
@@ -523,15 +523,15 @@ theorem sierpinski_pathological_family (Hcont : (#ℝ) = aleph 1) :
 
 /-- A family of sets in `ℝ` which only miss countably many points, but such that any point is
 contained in only countably many of them. -/
-def spf (Hcont : (#ℝ) = aleph 1) (x : ℝ) : Set ℝ :=
+def spf (Hcont : #ℝ = aleph 1) (x : ℝ) : Set ℝ :=
   (sierpinski_pathological_family Hcont).choose x
 #align counterexample.phillips_1940.spf Counterexample.Phillips1940.spf
 
-theorem countable_compl_spf (Hcont : (#ℝ) = aleph 1) (x : ℝ) : (univ \ spf Hcont x).Countable :=
+theorem countable_compl_spf (Hcont : #ℝ = aleph 1) (x : ℝ) : (univ \ spf Hcont x).Countable :=
   (sierpinski_pathological_family Hcont).choose_spec.1 x
 #align counterexample.phillips_1940.countable_compl_spf Counterexample.Phillips1940.countable_compl_spf
 
-theorem countable_spf_mem (Hcont : (#ℝ) = aleph 1) (y : ℝ) : {x | y ∈ spf Hcont x}.Countable :=
+theorem countable_spf_mem (Hcont : #ℝ = aleph 1) (y : ℝ) : {x | y ∈ spf Hcont x}.Countable :=
   (sierpinski_pathological_family Hcont).choose_spec.2 y
 #align counterexample.phillips_1940.countable_spf_mem Counterexample.Phillips1940.countable_spf_mem
 
@@ -552,11 +552,11 @@ which is large (it has countable complement), as in the Sierpinski pathological
 /-- A family of bounded functions `f_x` from `ℝ` (seen with the discrete topology) to `ℝ` (in fact
 taking values in `{0, 1}`), indexed by a real parameter `x`, corresponding to the characteristic
 functions of the different fibers of the Sierpinski pathological family -/
-def f (Hcont : (#ℝ) = aleph 1) (x : ℝ) : DiscreteCopy ℝ →ᵇ ℝ :=
+def f (Hcont : #ℝ = aleph 1) (x : ℝ) : DiscreteCopy ℝ →ᵇ ℝ :=
   ofNormedAddCommGroupDiscrete (indicator (spf Hcont x) 1) 1 (norm_indicator_le_one _)
 #align counterexample.phillips_1940.f Counterexample.Phillips1940.f
 
-theorem apply_f_eq_continuousPart (Hcont : (#ℝ) = aleph 1) (φ : (DiscreteCopy ℝ →ᵇ ℝ) →L[ℝ] ℝ)
+theorem apply_f_eq_continuousPart (Hcont : #ℝ = aleph 1) (φ : (DiscreteCopy ℝ →ᵇ ℝ) →L[ℝ] ℝ)
     (x : ℝ) (hx : φ.toBoundedAdditiveMeasure.discreteSupport ∩ spf Hcont x = ∅) :
     φ (f Hcont x) = φ.toBoundedAdditiveMeasure.continuousPart univ := by
   set ψ := φ.toBoundedAdditiveMeasure
@@ -567,7 +567,7 @@ theorem apply_f_eq_continuousPart (Hcont : (#ℝ) = aleph 1) (φ : (DiscreteCopy
     ψ.continuousPart_apply_eq_zero_of_countable _ (countable_compl_spf Hcont x), add_zero]
 #align counterexample.phillips_1940.apply_f_eq_continuous_part Counterexample.Phillips1940.apply_f_eq_continuousPart
 
-theorem countable_ne (Hcont : (#ℝ) = aleph 1) (φ : (DiscreteCopy ℝ →ᵇ ℝ) →L[ℝ] ℝ) :
+theorem countable_ne (Hcont : #ℝ = aleph 1) (φ : (DiscreteCopy ℝ →ᵇ ℝ) →L[ℝ] ℝ) :
     {x | φ.toBoundedAdditiveMeasure.continuousPart univ ≠ φ (f Hcont x)}.Countable := by
   have A :
     {x | φ.toBoundedAdditiveMeasure.continuousPart univ ≠ φ (f Hcont x)} ⊆
@@ -588,7 +588,7 @@ theorem countable_ne (Hcont : (#ℝ) = aleph 1) (φ : (DiscreteCopy ℝ →ᵇ 
   exact Countable.biUnion (countable_discreteSupport _) fun a _ => countable_spf_mem Hcont a
 #align counterexample.phillips_1940.countable_ne Counterexample.Phillips1940.countable_ne
 
-theorem comp_ae_eq_const (Hcont : (#ℝ) = aleph 1) (φ : (DiscreteCopy ℝ →ᵇ ℝ) →L[ℝ] ℝ) :
+theorem comp_ae_eq_const (Hcont : #ℝ = aleph 1) (φ : (DiscreteCopy ℝ →ᵇ ℝ) →L[ℝ] ℝ) :
     ∀ᵐ x ∂volume.restrict (Icc (0 : ℝ) 1),
       φ.toBoundedAdditiveMeasure.continuousPart univ = φ (f Hcont x) := by
   apply ae_restrict_of_ae
@@ -597,7 +597,7 @@ theorem comp_ae_eq_const (Hcont : (#ℝ) = aleph 1) (φ : (DiscreteCopy ℝ →
   simp only [imp_self, mem_setOf_eq, mem_compl_iff]
 #align counterexample.phillips_1940.comp_ae_eq_const Counterexample.Phillips1940.comp_ae_eq_const
 
-theorem integrable_comp (Hcont : (#ℝ) = aleph 1) (φ : (DiscreteCopy ℝ →ᵇ ℝ) →L[ℝ] ℝ) :
+theorem integrable_comp (Hcont : #ℝ = aleph 1) (φ : (DiscreteCopy ℝ →ᵇ ℝ) →L[ℝ] ℝ) :
     IntegrableOn (fun x => φ (f Hcont x)) (Icc 0 1) := by
   have :
     IntegrableOn (fun _ => φ.toBoundedAdditiveMeasure.continuousPart univ) (Icc (0 : ℝ) 1)
@@ -606,7 +606,7 @@ theorem integrable_comp (Hcont : (#ℝ) = aleph 1) (φ : (DiscreteCopy ℝ →
   apply Integrable.congr this (comp_ae_eq_const Hcont φ)
 #align counterexample.phillips_1940.integrable_comp Counterexample.Phillips1940.integrable_comp
 
-theorem integral_comp (Hcont : (#ℝ) = aleph 1) (φ : (DiscreteCopy ℝ →ᵇ ℝ) →L[ℝ] ℝ) :
+theorem integral_comp (Hcont : #ℝ = aleph 1) (φ : (DiscreteCopy ℝ →ᵇ ℝ) →L[ℝ] ℝ) :
     ∫ x in Icc 0 1, φ (f Hcont x) = φ.toBoundedAdditiveMeasure.continuousPart univ := by
   rw [← integral_congr_ae (comp_ae_eq_const Hcont φ)]
   simp
@@ -622,7 +622,7 @@ no Pettis integral.
 example : CompleteSpace (DiscreteCopy ℝ →ᵇ ℝ) := by infer_instance
 
 /-- The function `f Hcont : ℝ → (DiscreteCopy ℝ →ᵇ ℝ)` is scalarly measurable. -/
-theorem measurable_comp (Hcont : (#ℝ) = aleph 1) (φ : (DiscreteCopy ℝ →ᵇ ℝ) →L[ℝ] ℝ) :
+theorem measurable_comp (Hcont : #ℝ = aleph 1) (φ : (DiscreteCopy ℝ →ᵇ ℝ) →L[ℝ] ℝ) :
     Measurable fun x => φ (f Hcont x) := by
   have : Measurable fun _ : ℝ => φ.toBoundedAdditiveMeasure.continuousPart univ := measurable_const
   refine' this.measurable_of_countable_ne _
@@ -630,12 +630,12 @@ theorem measurable_comp (Hcont : (#ℝ) = aleph 1) (φ : (DiscreteCopy ℝ →
 #align counterexample.phillips_1940.measurable_comp Counterexample.Phillips1940.measurable_comp
 
 /-- The function `f Hcont : ℝ → (DiscreteCopy ℝ →ᵇ ℝ)` is uniformly bounded by `1` in norm. -/
-theorem norm_bound (Hcont : (#ℝ) = aleph 1) (x : ℝ) : ‖f Hcont x‖ ≤ 1 :=
+theorem norm_bound (Hcont : #ℝ = aleph 1) (x : ℝ) : ‖f Hcont x‖ ≤ 1 :=
   norm_ofNormedAddCommGroup_le _ zero_le_one (norm_indicator_le_one _)
 #align counterexample.phillips_1940.norm_bound Counterexample.Phillips1940.norm_bound
 
 /-- The function `f Hcont : ℝ → (DiscreteCopy ℝ →ᵇ ℝ)` has no Pettis integral. -/
-theorem no_pettis_integral (Hcont : (#ℝ) = aleph 1) :
+theorem no_pettis_integral (Hcont : #ℝ = aleph 1) :
     ¬∃ g : DiscreteCopy ℝ →ᵇ ℝ,
         ∀ φ : (DiscreteCopy ℝ →ᵇ ℝ) →L[ℝ] ℝ, ∫ x in Icc 0 1, φ (f Hcont x) = φ g := by
   rintro ⟨g, h⟩

@@ -296,7 +296,7 @@ theorem exists_discrete_support_nonpos (f : BoundedAdditiveMeasure α) :
   -- iterate the above construction, by adding at each step a set with measure close to maximal in
   -- the complement of already chosen points. This is the set `s n` at step `n`.
   let G : A → A := fun u => ⟨(↑u : Set α) ∪ ↑(F u), u.2.union (F u).2⟩
-  let s : ℕ → A := fun n => (G^[n]) empty
+  let s : ℕ → A := fun n => G^[n] empty
   -- We will get a contradiction from the fact that there is a countable set `u` with positive
   -- measure in the complement of `⋃ n, s n`.
   rcases h (⋃ n, ↑(s n)) (countable_iUnion fun n => (s n).2) with ⟨t, t_count, ht⟩

Rewrite the IMO 2019 q4 solution to make the "implicit" calc blocks (lots of lt_of_le_of_lt) explicit, then automate some proofs.

This is not a golf in the sense of decreasing the number of lines (maybe it is if you take into account the number of lines like

intros; rw [sub_nonneg]; apply pow_le_pow; norm_num; apply le_of_lt; rwa [← mem_range]

in the original). So, if desired, I can make this an additional proof rather than a replacement to the existing proof.