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Mathlib/Algebra/BigOperators/Finprod.lean

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@@ -545,6 +545,8 @@ theorem one_lt_finprod_cond {M : Type*} [CommMonoid M] [PartialOrder M] [IsOrder
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· aesop
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· simp +contextual
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@[deprecated (since := "2026-01-06")] alias finprod_cond_pos := finsum_cond_pos
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@[to_additive finsum_pos]
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theorem one_lt_finprod {M : Type*} [CommMonoid M] [PartialOrder M] [IsOrderedCancelMonoid M]
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{f : ι → M}

Mathlib/Algebra/Group/Irreducible/Indecomposable.lean

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@@ -111,6 +111,10 @@ lemma Submonoid.closure_image_isMulIndecomposable_baseOf [Finite ι]
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replace hjk : v i ∈ closure (v '' t) := hjk ▸ mul_mem hj' hk'
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exact hi₁ hjk
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@[deprecated (since := "2025-12-30")]
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alias Submonoid.closure_image_one_lt_and_isMulIndecomposable :=
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Submonoid.closure_image_isMulIndecomposable_baseOf
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@[to_additive]
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lemma Subgroup.closure_image_isMulIndecomposable_baseOf [Finite ι] [InvolutiveInv ι]
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[CommGroup S] [IsOrderedMonoid S]

Mathlib/Algebra/Polynomial/Derivative.lean

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@@ -401,6 +401,9 @@ noncomputable def derivativeFinsupp : R[X] →ₗ[R] ℕ →₀ R[X] where
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map_add' _ _ := by ext; simp
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map_smul' _ _ := by ext; simp
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@[deprecated (since := "2025-12-15")]
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alias derivativeFinsupp_apply_toFun := derivativeFinsupp_apply_apply
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@[simp]
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theorem support_derivativeFinsupp_subset_range {p : R[X]} {n : ℕ} (h : p.natDegree < n) :
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(derivativeFinsupp p).support ⊆ range n := by

Mathlib/Algebra/Polynomial/Roots.lean

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@@ -307,6 +307,8 @@ theorem roots_eq_of_degree_eq_card {S : Finset R}
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(hS : ∀ x ∈ S, p.eval x = 0) (hcard : S.card = p.degree) : p.roots = S.val :=
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roots_eq_of_degree_le_card_of_ne_zero hS (by lia) (by contrapose! hcard; simp [hcard])
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@[deprecated (since := "2025-12-16")] alias roots_eq_of_degree_le_card := roots_eq_of_degree_eq_card
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theorem roots_eq_of_natDegree_le_card_of_ne_zero {S : Finset R}
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(hS : ∀ x ∈ S, p.eval x = 0) (hcard : p.natDegree ≤ S.card) (hp : p ≠ 0) : p.roots = S.val :=
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roots_eq_of_degree_le_card_of_ne_zero hS (degree_le_of_natDegree_le hcard) hp

Mathlib/Analysis/Calculus/ImplicitContDiff.lean

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@@ -70,6 +70,12 @@ namespace IsContDiffImplicitAt
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variable
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{n : WithTop ℕ∞} {f : E × F → G} {f' : E × F →L[𝕜] G} {a : E × F}
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omit [CompleteSpace E] [CompleteSpace F] [CompleteSpace G] in
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@[deprecated IsContDiffImplicitAt.ne_zero (since := "2025-12-22")]
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theorem one_le (h : IsContDiffImplicitAt n f f' a) : 1 ≤ n := by
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rw [ENat.one_le_iff_ne_zero_withTop]
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exact h.ne_zero
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/-- We record the parameters of our specific case in order to apply the general implicit function
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theorem. -/
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def implicitFunctionData (h : IsContDiffImplicitAt n f f' a) :
@@ -105,10 +111,20 @@ lemma implicitFunctionData_pt (h : IsContDiffImplicitAt n f f' a) :
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lemma implicitFunctionData_leftFun_apply {h : IsContDiffImplicitAt n f f' a} {xy : E × F} :
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h.implicitFunctionData.leftFun xy = xy.1 := rfl
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@[deprecated "use simp" (since := "2026-01-08")]
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lemma implicitFunctionData_leftFun_pt (h : IsContDiffImplicitAt n f f' a) :
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h.implicitFunctionData.leftFun h.implicitFunctionData.pt = a.1 := by
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simp
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@[simp]
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lemma implicitFunctionData_rightFun_apply {h : IsContDiffImplicitAt n f f' a} {xy : E × F} :
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h.implicitFunctionData.rightFun xy = f xy := rfl
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@[deprecated "use simp" (since := "2026-01-08")]
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lemma implicitFunctionData_rightFun_pt (h : IsContDiffImplicitAt n f f' a) :
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h.implicitFunctionData.rightFun h.implicitFunctionData.pt = f a := by
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simp
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/-- The implicit function provided by the general theorem, from which we construct the more useful
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form `IsContDiffImplicitAt.implicitFunction`. -/
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noncomputable def implicitFunctionAux (h : IsContDiffImplicitAt n f f' a) : E → G → E × F :=

Mathlib/Analysis/Distribution/TemperedDistribution.lean

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@@ -413,6 +413,9 @@ theorem fourier_toTemperedDistributionCLM_eq (f : 𝓢(E, F)) :
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ext g
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simpa using integral_fourier_smul_eq g f
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@[deprecated (since := "2026-01-14")]
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alias fourierTransform_toTemperedDistributionCLM_eq := fourier_toTemperedDistributionCLM_eq
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/-- The distributional inverse Fourier transform and the classical inverse Fourier transform
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coincide on `𝓢(E, F)`. -/
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theorem fourierInv_toTemperedDistributionCLM_eq (f : 𝓢(E, F)) :
@@ -423,6 +426,9 @@ theorem fourierInv_toTemperedDistributionCLM_eq (f : 𝓢(E, F)) :
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rw [fourier_toTemperedDistributionCLM_eq]
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_ = _ := fourierInv_fourier_eq _
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@[deprecated (since := "2026-01-14")]
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alias fourierTransformInv_toTemperedDistributionCLM_eq := fourierInv_toTemperedDistributionCLM_eq
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end Fourier
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section DiracDelta

Mathlib/Analysis/Fourier/LpSpace.lean

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@@ -103,6 +103,9 @@ theorem SchwartzMap.toLp_fourier_eq (f : 𝓢(E, F)) : 𝓕 (f.toLp 2) = (𝓕 f
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rw [one_mul]
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exact (norm_fourier_toL2_eq f).le
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@[deprecated (since := "2025-12-31")]
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alias SchwartzMap.toLp_fourierTransform_eq := SchwartzMap.toLp_fourier_eq
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@[simp]
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theorem SchwartzMap.toLp_fourierInv_eq (f : 𝓢(E, F)) : 𝓕⁻ (f.toLp 2) = (𝓕⁻ f).toLp 2 := by
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apply LinearMap.extendOfNorm_eq
@@ -113,6 +116,9 @@ theorem SchwartzMap.toLp_fourierInv_eq (f : 𝓢(E, F)) : 𝓕⁻ (f.toLp 2) = (
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convert (norm_fourier_toL2_eq (𝓕⁻ f)).symm.le
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simp
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@[deprecated (since := "2025-12-31")]
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alias SchwartzMap.toLp_fourierTransformInv_eq := SchwartzMap.toLp_fourierInv_eq
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namespace MeasureTheory.Lp
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/-- The `𝓢'`-Fourier transform and the `L2`-Fourier transform coincide on `L2`. -/

Mathlib/Analysis/Fourier/Notation.lean

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@@ -138,6 +138,11 @@ def fourierₗ : E →ₗ[R] F where
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@[simp]
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lemma fourierₗ_apply (f : E) : fourierₗ R E f = 𝓕 f := rfl
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include R in
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variable (R) in
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lemma fourier_zero : 𝓕 (0 : E) = 0 :=
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(fourierₗ R E).map_zero
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variable [TopologicalSpace E] [TopologicalSpace F] [ContinuousFourier E F]
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variable (R E) in
@@ -165,6 +170,11 @@ def fourierInvₗ : E →ₗ[R] F where
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@[simp]
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lemma fourierInvₗ_apply (f : E) : fourierInvₗ R E f = 𝓕⁻ f := rfl
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include R in
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variable (R) in
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lemma fourierInv_zero : 𝓕⁻ (0 : E) = 0 :=
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(fourierInvₗ R E).map_zero
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variable [TopologicalSpace E] [TopologicalSpace F] [ContinuousFourierInv E F]
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variable (R E) in

Mathlib/Analysis/Meromorphic/Basic.lean

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@@ -330,6 +330,11 @@ protected theorem deriv [CompleteSpace E] {f : 𝕜 → E} {x : 𝕜} (h : Merom
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MeromorphicAt.meromorphicAt_congr this]
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fun_prop
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@[deprecated MeromorphicAt.deriv (since := "2025-12-21")]
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theorem fun_deriv [CompleteSpace E] {f : 𝕜 → E} {x : 𝕜} (h : MeromorphicAt f x) :
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MeromorphicAt (fun z ↦ _root_.deriv f z) x :=
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h.deriv
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/--
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Iterated derivatives of meromorphic functions are meromorphic.
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-/
@@ -340,6 +345,12 @@ Iterated derivatives of meromorphic functions are meromorphic.
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| zero => exact h
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| succ n IH => simpa only [Function.iterate_succ', Function.comp_apply] using IH.deriv
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@[deprecated MeromorphicAt.iterated_deriv (since := "2025-12-21")]
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theorem fun_iterated_deriv [CompleteSpace E] {n : ℕ} {f : 𝕜 → E} {x : 𝕜}
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(h : MeromorphicAt f x) :
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MeromorphicAt (fun z ↦ _root_.deriv^[n] f z) x :=
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h.iterated_deriv
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end MeromorphicAt
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section smul_iff
@@ -522,11 +533,21 @@ include hf in
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/-- Derivatives of meromorphic functions are meromorphic. -/
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protected theorem deriv [CompleteSpace E] : MeromorphicOn (deriv f) U := fun z hz ↦ (hf z hz).deriv
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include hf in
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@[deprecated MeromorphicOn.deriv (since := "2025-12-21")]
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theorem fun_deriv [CompleteSpace E] : MeromorphicOn (fun z ↦ _root_.deriv f z) U := hf.deriv
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include hf in
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/-- Iterated derivatives of meromorphic functions are meromorphic. -/
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theorem iterated_deriv [CompleteSpace E] {n : ℕ} : MeromorphicOn (_root_.deriv^[n] f) U :=
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fun z hz ↦ (hf z hz).iterated_deriv
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include hf in
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@[deprecated MeromorphicOn.iterated_deriv (since := "2025-12-21")]
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theorem fun_iterated_deriv [CompleteSpace E] {n : ℕ} :
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MeromorphicOn (fun z ↦ _root_.deriv^[n] f z) U :=
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hf.iterated_deriv
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end arithmetic
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include hf in
@@ -636,6 +657,8 @@ theorem countable_compl_analyticAt [SecondCountableTopology 𝕜] [CompleteSpace
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@[deprecated (since := "2025-12-21")] alias MeromorphicOn.countable_compl_analyticAt :=
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countable_compl_analyticAt
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@[deprecated (since := "2025-12-21")] alias _root_.MeromorphicOn.countable_compl_analyticAt :=
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countable_compl_analyticAt
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/--
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Meromorphic functions are measurable.
@@ -652,5 +675,6 @@ theorem measurable [MeasurableSpace 𝕜] [SecondCountableTopology 𝕜] [BorelS
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(by simp [-mem_compl_iff]) h₃.restrict.measurable (measurable_of_countable _)
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@[deprecated (since := "2025-12-21")] alias MeromorphicOn.measurable := measurable
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@[deprecated (since := "2025-12-21")] alias _root_.MeromorphicOn.measurable := measurable
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end Meromorphic

Mathlib/Analysis/Normed/Lp/ProdLp.lean

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@@ -1199,6 +1199,8 @@ def withLpProdCongr (f : α ≃ₗᵢ[𝕜] α') (g : β ≃ₗᵢ[𝕜] β') :
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__ := (f.toLinearEquiv.prodCongr g.toLinearEquiv).withLpCongr p
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norm_map' := (f.toLinearIsometry.withLpProdMap p g.toLinearIsometry).norm_map
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1202+
@[deprecated (since := "2025-12-22")] alias _root_.LinearIsometry.withLpProdCongr := withLpProdCongr
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/-- Commutativity of the `L^p` product as a linear isometric equivalence. -/
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def withLpProdComm : WithLp p (α × β) ≃ₗᵢ[𝕜] WithLp p (β × α) where
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__ := (LinearEquiv.prodComm 𝕜 α β).withLpCongr p

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