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[Merged by Bors] - chore: remove unnecessary @[eqns] attributes #11460

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4 changes: 0 additions & 4 deletions Mathlib/Computability/TMToPartrec.lean
Original file line number Diff line number Diff line change
Expand Up @@ -1240,9 +1240,6 @@ def K'.elim (a b c d : List Γ') : K' → List Γ'
| K'.stack => d
#align turing.partrec_to_TM2.K'.elim Turing.PartrecToTM2.K'.elim

/- Porting note: The equation lemma of `elim` simplifies to `match` structures. To prevent this,
we replace equation lemmas of `elim`. -/

theorem K'.elim_main (a b c d) : K'.elim a b c d K'.main = a := rfl

theorem K'.elim_rev (a b c d) : K'.elim a b c d K'.rev = b := rfl
Expand All @@ -1251,7 +1248,6 @@ theorem K'.elim_aux (a b c d) : K'.elim a b c d K'.aux = c := rfl

theorem K'.elim_stack (a b c d) : K'.elim a b c d K'.stack = d := rfl

attribute [eqns K'.elim_main K'.elim_rev K'.elim_aux K'.elim_stack] K'.elim
attribute [simp] K'.elim

@[simp]
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2 changes: 1 addition & 1 deletion Mathlib/MeasureTheory/Decomposition/RadonNikodym.lean
Original file line number Diff line number Diff line change
Expand Up @@ -409,7 +409,7 @@ theorem withDensityᵥ_rnDeriv_eq (s : SignedMeasure α) (μ : Measure α) [Sigm
rw [absolutelyContinuous_ennreal_iff, (_ : μ.toENNRealVectorMeasure.ennrealToMeasure = μ),
totalVariation_absolutelyContinuous_iff] at h
· ext1 i hi
rw [withDensityᵥ_apply (integrable_rnDeriv _ _) hi, rnDeriv, integral_sub,
rw [withDensityᵥ_apply (integrable_rnDeriv _ _) hi, rnDeriv_def, integral_sub,
set_integral_toReal_rnDeriv h.1 i, set_integral_toReal_rnDeriv h.2 i]
· conv_rhs => rw [← s.toSignedMeasure_toJordanDecomposition]
erw [VectorMeasure.sub_apply]
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8 changes: 2 additions & 6 deletions Mathlib/MeasureTheory/Decomposition/SignedLebesgue.lean
Original file line number Diff line number Diff line change
Expand Up @@ -178,20 +178,16 @@ def rnDeriv (s : SignedMeasure α) (μ : Measure α) : α → ℝ := fun x =>
(s.toJordanDecomposition.negPart.rnDeriv μ x).toReal
#align measure_theory.signed_measure.rn_deriv MeasureTheory.SignedMeasure.rnDeriv

-- Porting note: The generated equation theorem is the form of `rnDeriv s μ x`.

theorem rnDeriv_def (s : SignedMeasure α) (μ : Measure α) : rnDeriv s μ = fun x =>
(s.toJordanDecomposition.posPart.rnDeriv μ x).toReal -
(s.toJordanDecomposition.negPart.rnDeriv μ x).toReal :=
rfl

attribute [eqns rnDeriv_def] rnDeriv

variable {s t : SignedMeasure α}

@[measurability]
theorem measurable_rnDeriv (s : SignedMeasure α) (μ : Measure α) : Measurable (rnDeriv s μ) := by
rw [rnDeriv]
rw [rnDeriv_def]
measurability
#align measure_theory.signed_measure.measurable_rn_deriv MeasureTheory.SignedMeasure.measurable_rnDeriv

Expand All @@ -213,7 +209,7 @@ theorem singularPart_add_withDensity_rnDeriv_eq [s.HaveLebesgueDecomposition μ]
s.singularPart μ + μ.withDensityᵥ (s.rnDeriv μ) = s := by
conv_rhs =>
rw [← toSignedMeasure_toJordanDecomposition s, JordanDecomposition.toSignedMeasure]
rw [singularPart, rnDeriv,
rw [singularPart, rnDeriv_def,
withDensityᵥ_sub' (integrable_toReal_of_lintegral_ne_top _ _)
(integrable_toReal_of_lintegral_ne_top _ _),
withDensityᵥ_toReal, withDensityᵥ_toReal, sub_eq_add_neg, sub_eq_add_neg,
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4 changes: 0 additions & 4 deletions Mathlib/MeasureTheory/Function/L1Space.lean
Original file line number Diff line number Diff line change
Expand Up @@ -112,8 +112,6 @@ theorem hasFiniteIntegral_def {_ : MeasurableSpace α} (f : α → β) (μ : Mea
HasFiniteIntegral f μ ↔ ((∫⁻ a, ‖f a‖₊ ∂μ) < ∞) :=
Iff.rfl

attribute [eqns hasFiniteIntegral_def] HasFiniteIntegral

theorem hasFiniteIntegral_iff_norm (f : α → β) :
HasFiniteIntegral f μ ↔ (∫⁻ a, ENNReal.ofReal ‖f a‖ ∂μ) < ∞ := by
simp only [HasFiniteIntegral, ofReal_norm_eq_coe_nnnorm]
Expand Down Expand Up @@ -446,8 +444,6 @@ theorem integrable_def {α} {_ : MeasurableSpace α} (f : α → β) (μ : Measu
Integrable f μ ↔ (AEStronglyMeasurable f μ ∧ HasFiniteIntegral f μ) :=
Iff.rfl

attribute [eqns integrable_def] Integrable

theorem memℒp_one_iff_integrable {f : α → β} : Memℒp f 1 μ ↔ Integrable f μ := by
simp_rw [Integrable, HasFiniteIntegral, Memℒp, snorm_one_eq_lintegral_nnnorm]
#align measure_theory.mem_ℒp_one_iff_integrable MeasureTheory.memℒp_one_iff_integrable
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7 changes: 0 additions & 7 deletions Mathlib/MeasureTheory/Function/LpSeminorm/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -109,13 +109,6 @@ def Memℒp {α} {_ : MeasurableSpace α} (f : α → E) (p : ℝ≥0∞)
AEStronglyMeasurable f μ ∧ snorm f p μ < ∞
#align measure_theory.mem_ℒp MeasureTheory.Memℒp

-- Porting note (#11215): TODO Delete this when leanprover/lean4#2243 is fixed.
theorem memℒp_def {α} {_ : MeasurableSpace α} (f : α → E) (p : ℝ≥0∞) (μ : Measure α) :
Memℒp f p μ ↔ (AEStronglyMeasurable f μ ∧ snorm f p μ < ∞) :=
Iff.rfl

attribute [eqns memℒp_def] Memℒp

theorem Memℒp.aestronglyMeasurable {f : α → E} {p : ℝ≥0∞} (h : Memℒp f p μ) :
AEStronglyMeasurable f μ :=
h.1
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2 changes: 0 additions & 2 deletions Mathlib/MeasureTheory/Integral/IntegrableOn.lean
Original file line number Diff line number Diff line change
Expand Up @@ -96,8 +96,6 @@ theorem integrableOn_def (f : α → E) (s : Set α) (μ : Measure α) :
IntegrableOn f s μ ↔ Integrable f (μ.restrict s) :=
Iff.rfl

attribute [eqns integrableOn_def] IntegrableOn

theorem IntegrableOn.integrable (h : IntegrableOn f s μ) : Integrable f (μ.restrict s) :=
h
#align measure_theory.integrable_on.integrable MeasureTheory.IntegrableOn.integrable
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