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[Merged by Bors] - refactor: move disjoint_sdiff_inter #12021

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[Merged by Bors] - refactor: move disjoint_sdiff_inter #12021

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eb98f58
refactor: move disjoint_sdiff_inter
mo271 Apr 8, 2024
3246426
cleanup imports
mo271 Apr 8, 2024
25724ae
Update Mathlib/Data/Set/Basic.lean
mo271 Apr 11, 2024
e94da97
Update Mathlib/Data/Set/Basic.lean
mo271 Apr 11, 2024
8d8422d
fix build
mo271 Apr 13, 2024
9e09320
Update Mathlib/MeasureTheory/Integral/PeakFunction.lean
mo271 Apr 13, 2024
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5 changes: 5 additions & 0 deletions Mathlib/Data/Set/Basic.lean
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Expand Up @@ -1575,6 +1575,11 @@ lemma disjoint_sdiff_left : Disjoint (t \ s) s := disjoint_sdiff_self_left
lemma disjoint_sdiff_right : Disjoint s (t \ s) := disjoint_sdiff_self_right
#align set.disjoint_sdiff_right Set.disjoint_sdiff_right

-- TODO: prove this in terms of a lattice lemma
theorem disjoint_sdiff_inter : Disjoint (s \ t) (s ∩ t) :=
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disjoint_of_subset_right (inter_subset_right _ _) disjoint_sdiff_left
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#align set.disjoint_sdiff_inter Set.disjoint_sdiff_inter

theorem diff_union_diff_cancel (hts : t ⊆ s) (hut : u ⊆ t) : s \ t ∪ t \ u = s \ u :=
sdiff_sup_sdiff_cancel hts hut
#align set.diff_union_diff_cancel Set.diff_union_diff_cancel
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14 changes: 1 addition & 13 deletions Mathlib/MeasureTheory/Integral/PeakFunction.lean
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Expand Up @@ -3,12 +3,7 @@ Copyright (c) 2023 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.MeasureTheory.Integral.SetIntegral
import Mathlib.MeasureTheory.Function.LocallyIntegrable
import Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar
import Mathlib.MeasureTheory.Integral.IntegralEqImproper
import Mathlib.MeasureTheory.Group.Integral
import Mathlib.MeasureTheory.Measure.Haar.Unique

#align_import measure_theory.integral.peak_function from "leanprover-community/mathlib"@"13b0d72fd8533ba459ac66e9a885e35ffabb32b2"

Expand Down Expand Up @@ -44,13 +39,6 @@ open Set Filter MeasureTheory MeasureTheory.Measure TopologicalSpace Metric

open scoped Topology ENNReal

/-- This lemma exists for finsets, but not for sets currently. porting note: move to
data.set.basic after the port. -/
theorem Set.disjoint_sdiff_inter {α : Type*} (s t : Set α) : Disjoint (s \ t) (s ∩ t) :=
disjoint_of_subset_right (inter_subset_right _ _) disjoint_sdiff_left
#align set.disjoint_sdiff_inter Set.disjoint_sdiff_inter


/-!
### General convergent result for integrals against a sequence of peak functions
-/
Expand Down Expand Up @@ -186,7 +174,7 @@ theorem tendsto_set_integral_peak_smul_of_integrableOn_of_tendsto_aux
‖∫ x in s, φ i x • g x ∂μ‖ =
‖(∫ x in s \ u, φ i x • g x ∂μ) + ∫ x in s ∩ u, φ i x • g x ∂μ‖ := by
conv_lhs => rw [← diff_union_inter s u]
rw [integral_union (disjoint_sdiff_inter _ _) (hs.inter u_open.measurableSet)
rw [integral_union disjoint_sdiff_inter (hs.inter u_open.measurableSet)
(h''i.mono_set (diff_subset _ _)) (h''i.mono_set (inter_subset_left _ _))]
_ ≤ ‖∫ x in s \ u, φ i x • g x ∂μ‖ + ‖∫ x in s ∩ u, φ i x • g x ∂μ‖ := (norm_add_le _ _)
_ ≤ (δ * ∫ x in s, ‖g x‖ ∂μ) + 2 * δ := add_le_add C B
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