diff --git a/Mathlib/Analysis/SpecialFunctions/Gaussian.lean b/Mathlib/Analysis/SpecialFunctions/Gaussian.lean index 1dae80d20c38f..5a738b21716c8 100644 --- a/Mathlib/Analysis/SpecialFunctions/Gaussian.lean +++ b/Mathlib/Analysis/SpecialFunctions/Gaussian.lean @@ -118,7 +118,7 @@ theorem integrableOn_rpow_mul_exp_neg_mul_rpow {p s b : ℝ} (hs : -1 < s) (hp : rpow_neg_one, mul_inv_cancel_left₀] all_goals linarith [mem_Ioi.mp hx] refine Integrable.const_mul ?_ _ - rw [← integrableOn_def] + rw [← IntegrableOn] exact integrableOn_rpow_mul_exp_neg_rpow hs hp theorem integrableOn_rpow_mul_exp_neg_mul_sq {b : ℝ} (hb : 0 < b) {s : ℝ} (hs : -1 < s) : diff --git a/Mathlib/Computability/TMToPartrec.lean b/Mathlib/Computability/TMToPartrec.lean index 2d2157c403462..fe5a802203321 100644 --- a/Mathlib/Computability/TMToPartrec.lean +++ b/Mathlib/Computability/TMToPartrec.lean @@ -1240,8 +1240,7 @@ 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`. -/ +-- The equation lemma of `elim` simplifies to `match` structures. theorem K'.elim_main (a b c d) : K'.elim a b c d K'.main = a := rfl @@ -1251,7 +1250,6 @@ 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] diff --git a/Mathlib/MeasureTheory/Decomposition/RadonNikodym.lean b/Mathlib/MeasureTheory/Decomposition/RadonNikodym.lean index b0287cdfd5b78..d9e9cfc91b42f 100644 --- a/Mathlib/MeasureTheory/Decomposition/RadonNikodym.lean +++ b/Mathlib/MeasureTheory/Decomposition/RadonNikodym.lean @@ -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] diff --git a/Mathlib/MeasureTheory/Decomposition/SignedLebesgue.lean b/Mathlib/MeasureTheory/Decomposition/SignedLebesgue.lean index a5b8a1c4047fd..8c43a934ad08c 100644 --- a/Mathlib/MeasureTheory/Decomposition/SignedLebesgue.lean +++ b/Mathlib/MeasureTheory/Decomposition/SignedLebesgue.lean @@ -178,20 +178,17 @@ 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`. - +-- 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 @@ -213,7 +210,7 @@ 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, diff --git a/Mathlib/MeasureTheory/Function/L1Space.lean b/Mathlib/MeasureTheory/Function/L1Space.lean index 8d0c6a7304e5c..2ed79069a585c 100644 --- a/Mathlib/MeasureTheory/Function/L1Space.lean +++ b/Mathlib/MeasureTheory/Function/L1Space.lean @@ -110,8 +110,6 @@ 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] @@ -440,12 +438,6 @@ def Integrable {α} {_ : MeasurableSpace α} (f : α → β) (μ : Measure α := AEStronglyMeasurable f μ ∧ HasFiniteIntegral f μ #align measure_theory.integrable MeasureTheory.Integrable -theorem integrable_def {α} {_ : MeasurableSpace α} (f : α → β) (μ : Measure α) : - 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 diff --git a/Mathlib/MeasureTheory/Function/LpSeminorm/Basic.lean b/Mathlib/MeasureTheory/Function/LpSeminorm/Basic.lean index e4c7b7f0ead0e..b3f587301859a 100644 --- a/Mathlib/MeasureTheory/Function/LpSeminorm/Basic.lean +++ b/Mathlib/MeasureTheory/Function/LpSeminorm/Basic.lean @@ -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 diff --git a/Mathlib/MeasureTheory/Integral/IntegrableOn.lean b/Mathlib/MeasureTheory/Integral/IntegrableOn.lean index b5a6d52bae931..b3f433032c923 100644 --- a/Mathlib/MeasureTheory/Integral/IntegrableOn.lean +++ b/Mathlib/MeasureTheory/Integral/IntegrableOn.lean @@ -91,13 +91,6 @@ def IntegrableOn (f : α → E) (s : Set α) (μ : Measure α := by volume_tac) Integrable f (μ.restrict s) #align measure_theory.integrable_on MeasureTheory.IntegrableOn --- Porting note (#11215): TODO Delete this when leanprover/lean4#2243 is fixed. -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 diff --git a/Mathlib/NumberTheory/LSeries/AbstractFuncEq.lean b/Mathlib/NumberTheory/LSeries/AbstractFuncEq.lean index a39e97ff26d35..39c07dc24008f 100644 --- a/Mathlib/NumberTheory/LSeries/AbstractFuncEq.lean +++ b/Mathlib/NumberTheory/LSeries/AbstractFuncEq.lean @@ -360,10 +360,10 @@ lemma f_modif_aux2 {s : ℂ} (hs : P.k < re s) : - P.ε • (∫ (x : ℝ) in Ioc 0 1, (x : ℂ) ^ (s - P.k - 1)) • P.g₀ := by rw [integral_sub, integral_smul, integral_smul_const, integral_smul_const] · apply Integrable.smul_const - rw [← integrableOn_def, ← intervalIntegrable_iff_integrableOn_Ioc_of_le zero_le_one] + rw [← IntegrableOn, ← intervalIntegrable_iff_integrableOn_Ioc_of_le zero_le_one] exact intervalIntegral.intervalIntegrable_cpow' h_re1 · refine (Integrable.smul_const ?_ _).smul _ - rw [← integrableOn_def, ← intervalIntegrable_iff_integrableOn_Ioc_of_le zero_le_one] + rw [← IntegrableOn, ← intervalIntegrable_iff_integrableOn_Ioc_of_le zero_le_one] exact intervalIntegral.intervalIntegrable_cpow' h_re2 _ = _ := by simp_rw [← intervalIntegral.integral_of_le zero_le_one, integral_cpow (Or.inl h_re1), integral_cpow (Or.inl h_re2), ofReal_zero, ofReal_one, diff --git a/Mathlib/Probability/Distributions/Exponential.lean b/Mathlib/Probability/Distributions/Exponential.lean index 0e032b448eeff..e080e5e42c661 100644 --- a/Mathlib/Probability/Distributions/Exponential.lean +++ b/Mathlib/Probability/Distributions/Exponential.lean @@ -156,7 +156,7 @@ lemma lintegral_exponentialPDF_eq_antiDeriv {r : ℝ} (hr : 0 < r) (x : ℝ) : · simp only [neg_mul, one_mul] exact fun _ _ ↦ HasDerivAt.hasDerivWithinAt hasDerivAt_neg_exp_mul_exp · apply Integrable.aestronglyMeasurable (Integrable.const_mul _ _) - rw [← integrableOn_def, integrableOn_Icc_iff_integrableOn_Ioc] + rw [← IntegrableOn, integrableOn_Icc_iff_integrableOn_Ioc] exact exp_neg_integrableOn_Ioc hr · refine ne_of_lt (IntegrableOn.set_lintegral_lt_top ?_) rw [integrableOn_Icc_iff_integrableOn_Ioc]