feat(Topology/Algebra/InfiniteSum): Generalize ENNReal lemmas

[Jun2M]

This PR generalizes many theorems in Topology/Algebra/InfiniteSum/ENNReal.lean from ENNREal to any type that satisfies a list of order-related instances, mostly
[CommMonoid α] [CompleteLattice α] [CanonicallyOrderedMul α] [TopologicalSpace α] [SupConvergenceClass α]

Deprecation of the original ENNReal lemmas are done in the next PR: #38193.

Related Zulip thread: #Is there code for X? > Summing ENats without topology

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[github-actions]

PR summary bcf50344be

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Topology.Algebra.InfiniteSum.Order	1174	1179	+5 (+0.43%)
Mathlib.MeasureTheory.OuterMeasure.OfFunction	1466	1467	+1 (+0.07%)
Mathlib.MeasureTheory.Measure.MeasureSpace	1489	1490	+1 (+0.07%)

Import changes for all files

Files	Import difference
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Mathlib.NumberTheory.Harmonic.GammaDeriv Mathlib.NumberTheory.Harmonic.ZetaAsymp Mathlib.NumberTheory.Height.Basic Mathlib.NumberTheory.Height.MvPolynomial Mathlib.NumberTheory.Height.NumberField Mathlib.NumberTheory.Height.Projectivization Mathlib.NumberTheory.JacobiSum.Basic Mathlib.NumberTheory.LSeries.AbstractFuncEq Mathlib.NumberTheory.LSeries.Basic Mathlib.NumberTheory.LSeries.Convergence Mathlib.NumberTheory.LSeries.Convolution Mathlib.NumberTheory.LSeries.Deriv Mathlib.NumberTheory.LSeries.DirichletContinuation Mathlib.NumberTheory.LSeries.Dirichlet Mathlib.NumberTheory.LSeries.HurwitzZetaEven Mathlib.NumberTheory.LSeries.HurwitzZetaOdd Mathlib.NumberTheory.LSeries.HurwitzZetaValues Mathlib.NumberTheory.LSeries.HurwitzZeta Mathlib.NumberTheory.LSeries.Injectivity Mathlib.NumberTheory.LSeries.Linearity Mathlib.NumberTheory.LSeries.MellinEqDirichlet Mathlib.NumberTheory.LSeries.Nonvanishing Mathlib.NumberTheory.LSeries.Positivity Mathlib.NumberTheory.LSeries.PrimesInAP 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Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Defs Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.MDifferentiable Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform Mathlib.NumberTheory.ModularForms.EisensteinSeries.IsBoundedAtImInfty Mathlib.NumberTheory.ModularForms.EisensteinSeries.MDifferentiable Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable Mathlib.NumberTheory.ModularForms.EisensteinSeries.UniformConvergence Mathlib.NumberTheory.ModularForms.Identities Mathlib.NumberTheory.ModularForms.JacobiTheta.Bounds Mathlib.NumberTheory.ModularForms.JacobiTheta.Manifold Mathlib.NumberTheory.ModularForms.JacobiTheta.OneVariable Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable Mathlib.NumberTheory.ModularForms.LevelOne Mathlib.NumberTheory.ModularForms.NormTrace Mathlib.NumberTheory.ModularForms.Petersson 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Mathlib.NumberTheory.NumberField.Cyclotomic.Embeddings Mathlib.NumberTheory.NumberField.Cyclotomic.Galois Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal Mathlib.NumberTheory.NumberField.Cyclotomic.PID Mathlib.NumberTheory.NumberField.Cyclotomic.Three Mathlib.NumberTheory.NumberField.DedekindZeta Mathlib.NumberTheory.NumberField.Discriminant.Basic Mathlib.NumberTheory.NumberField.Discriminant.Different Mathlib.NumberTheory.NumberField.EquivReindex Mathlib.NumberTheory.NumberField.FinitePlaces Mathlib.NumberTheory.NumberField.House Mathlib.NumberTheory.NumberField.Ideal.Asymptotics Mathlib.NumberTheory.NumberField.Ideal.Basic Mathlib.NumberTheory.NumberField.InfiniteAdeleRing Mathlib.NumberTheory.NumberField.InfinitePlace.Basic Mathlib.NumberTheory.NumberField.InfinitePlace.Completion Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex Mathlib.NumberTheory.NumberField.ProductFormula Mathlib.NumberTheory.NumberField.Units.Basic Mathlib.NumberTheory.NumberField.Units.DirichletTheorem Mathlib.NumberTheory.NumberField.Units.Regulator Mathlib.NumberTheory.Ostrowski Mathlib.NumberTheory.Padics.AddChar Mathlib.NumberTheory.Padics.Complex Mathlib.NumberTheory.Padics.HeightOneSpectrum Mathlib.NumberTheory.Padics.Hensel Mathlib.NumberTheory.Padics.MahlerBasis Mathlib.NumberTheory.Padics.ProperSpace Mathlib.NumberTheory.Padics.ValuativeRel Mathlib.NumberTheory.Padics.WithVal Mathlib.NumberTheory.Pell Mathlib.NumberTheory.PrimesCongruentOne Mathlib.NumberTheory.Rayleigh Mathlib.NumberTheory.Real.GoldenRatio Mathlib.NumberTheory.Real.Irrational Mathlib.NumberTheory.SiegelsLemma Mathlib.NumberTheory.SumPrimeReciprocals Mathlib.NumberTheory.Transcendental.Lindemann.AnalyticalPart Mathlib.NumberTheory.Transcendental.Liouville.Basic Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleNumber 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Mathlib.Probability.Distributions.Gamma Mathlib.Probability.Distributions.Gaussian.Basic Mathlib.Probability.Distributions.Gaussian.CharFun Mathlib.Probability.Distributions.Gaussian.Fernique Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Def Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Def Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Independence Mathlib.Probability.Distributions.Gaussian.Multivariate Mathlib.Probability.Distributions.Gaussian.Real Mathlib.Probability.Distributions.Geometric Mathlib.Probability.Distributions.Pareto Mathlib.Probability.Distributions.Poisson.Basic Mathlib.Probability.Distributions.Poisson.PoissonLimitThm Mathlib.Probability.Distributions.SetBernoulli Mathlib.Probability.Distributions.TwoValued 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Mathlib.Probability.Kernel.Disintegration.CDFToKernel Mathlib.Probability.Kernel.Disintegration.CondCDF Mathlib.Probability.Kernel.Disintegration.Density Mathlib.Probability.Kernel.Disintegration.Integral Mathlib.Probability.Kernel.Disintegration.MeasurableStieltjes Mathlib.Probability.Kernel.Disintegration.StandardBorel Mathlib.Probability.Kernel.Disintegration.Unique Mathlib.Probability.Kernel.Integral Mathlib.Probability.Kernel.Invariance Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj Mathlib.Probability.Kernel.IonescuTulcea.Traj Mathlib.Probability.Kernel.Irreducible Mathlib.Probability.Kernel.MeasurableIntegral Mathlib.Probability.Kernel.MeasurableLIntegral Mathlib.Probability.Kernel.Posterior Mathlib.Probability.Kernel.Proper Mathlib.Probability.Kernel.RadonNikodym Mathlib.Probability.Kernel.Representation Mathlib.Probability.Kernel.SetIntegral Mathlib.Probability.Kernel.WithDensity Mathlib.Probability.Martingale.Basic Mathlib.Probability.Martingale.BorelCantelli Mathlib.Probability.Martingale.Centering Mathlib.Probability.Martingale.Convergence Mathlib.Probability.Martingale.OptionalSampling Mathlib.Probability.Martingale.OptionalStopping Mathlib.Probability.Martingale.Upcrossing Mathlib.Probability.Moments.Basic Mathlib.Probability.Moments.ComplexMGF Mathlib.Probability.Moments.CovarianceBilinDual Mathlib.Probability.Moments.CovarianceBilin Mathlib.Probability.Moments.Covariance Mathlib.Probability.Moments.IntegrableExpMul Mathlib.Probability.Moments.MGFAnalytic Mathlib.Probability.Moments.SubGaussian Mathlib.Probability.Moments.Tilted Mathlib.Probability.Moments.Variance Mathlib.Probability.Notation Mathlib.Probability.ProbabilityMassFunction.Basic Mathlib.Probability.ProbabilityMassFunction.Binomial Mathlib.Probability.ProbabilityMassFunction.Constructions Mathlib.Probability.ProbabilityMassFunction.Integrals Mathlib.Probability.ProbabilityMassFunction.Monad Mathlib.Probability.Process.Adapted Mathlib.Probability.Process.Filtration 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Mathlib.RingTheory.Polynomial.Selmer Mathlib.RingTheory.PowerSeries.Restricted Mathlib.RingTheory.RootsOfUnity.AlgebraicallyClosed Mathlib.RingTheory.RootsOfUnity.Complex Mathlib.RingTheory.Teichmuller Mathlib.RingTheory.Valuation.Discrete.RankOne Mathlib.RingTheory.Valuation.DiscreteValuativeRel Mathlib.RingTheory.Valuation.RankOne Mathlib.Tactic.ComputeAsymptotics.Lemmas Mathlib.Tactic.ComputeAsymptotics.Multiseries.Basis Mathlib.Tactic.ComputeAsymptotics.Multiseries.Corecursion Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs Mathlib.Tactic.ComputeAsymptotics.Multiseries.Majorized Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Basic Mathlib.Tactic.NormNum.Irrational Mathlib.Tactic.NormNum.LegendreSymbol Mathlib.Tactic.NormNum.RealSqrt Mathlib.Tactic Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic Mathlib.Topology.Algebra.Category.ProfiniteGrp.Completion Mathlib.Topology.Algebra.Category.ProfiniteGrp.Limits Mathlib.Topology.Algebra.InfiniteSum.ENNReal 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Mathlib.Topology.Category.Compactum Mathlib.Topology.Category.DeltaGenerated Mathlib.Topology.Category.LightProfinite.AsLimit Mathlib.Topology.Category.LightProfinite.Basic Mathlib.Topology.Category.LightProfinite.Cartesian Mathlib.Topology.Category.LightProfinite.EffectiveEpi Mathlib.Topology.Category.LightProfinite.Extend Mathlib.Topology.Category.LightProfinite.Injective Mathlib.Topology.Category.LightProfinite.Limits Mathlib.Topology.Category.LightProfinite.Sequence Mathlib.Topology.Category.Locale Mathlib.Topology.Category.Profinite.AsLimit Mathlib.Topology.Category.Profinite.Basic Mathlib.Topology.Category.Profinite.CofilteredLimit Mathlib.Topology.Category.Profinite.EffectiveEpi Mathlib.Topology.Category.Profinite.Extend Mathlib.Topology.Category.Profinite.Limits Mathlib.Topology.Category.Profinite.Nobeling.Basic Mathlib.Topology.Category.Profinite.Nobeling.Induction Mathlib.Topology.Category.Profinite.Nobeling.Span Mathlib.Topology.Category.Profinite.Nobeling.Successor Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit Mathlib.Topology.Category.Profinite.Product Mathlib.Topology.Category.Profinite.Projective Mathlib.Topology.Category.Stonean.Adjunctions Mathlib.Topology.Category.Stonean.Basic Mathlib.Topology.Category.Stonean.EffectiveEpi Mathlib.Topology.Category.Stonean.Limits Mathlib.Topology.Category.TopCat.Sphere Mathlib.Topology.Compactification.OnePoint.Sphere Mathlib.Topology.Compactness.CompactlyGeneratedSpace Mathlib.Topology.Compactness.DeltaGeneratedSpace Mathlib.Topology.ContinuousMap.Bounded.Normed Mathlib.Topology.ContinuousMap.Bounded.Star Mathlib.Topology.ContinuousMap.BoundedCompactlySupported Mathlib.Topology.ContinuousMap.Compact Mathlib.Topology.ContinuousMap.CompactlySupported Mathlib.Topology.ContinuousMap.ContinuousMapZero Mathlib.Topology.ContinuousMap.ContinuousSqrt Mathlib.Topology.ContinuousMap.Ideals Mathlib.Topology.ContinuousMap.StarOrdered Mathlib.Topology.ContinuousMap.StoneWeierstrass 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Mathlib.Topology.MetricSpace.HolderNorm Mathlib.Topology.MetricSpace.Holder Mathlib.Topology.MetricSpace.Kuratowski Mathlib.Topology.MetricSpace.PartitionOfUnity Mathlib.Topology.MetricSpace.Perfect Mathlib.Topology.MetricSpace.PiNat Mathlib.Topology.MetricSpace.Polish Mathlib.Topology.MetricSpace.Snowflaking Mathlib.Topology.MetricSpace.ThickenedIndicator Mathlib.Topology.MetricSpace.Thickening Mathlib.Topology.MetricSpace.Ultra.ContinuousMaps Mathlib.Topology.MetricSpace.UniformConvergence Mathlib.Topology.Metrizable.Urysohn Mathlib.Topology.Order.Category.FrameAdjunction Mathlib.Topology.PartitionOfUnity Mathlib.Topology.Semicontinuity.Basic Mathlib.Topology.Semicontinuity.Lindelof Mathlib.Topology.Separation.CompletelyRegular Mathlib.Topology.Separation.Lemmas Mathlib.Topology.Sion Mathlib.Topology.TietzeExtension Mathlib.Topology.UniformSpace.Uniformizable Mathlib.Topology.UrysohnsBounded Mathlib.Topology.UrysohnsLemma Mathlib.Topology.VectorBundle.Basic Mathlib.Topology.VectorBundle.Constructions Mathlib.Topology.VectorBundle.FiniteDimensional Mathlib.Topology.VectorBundle.Hom Mathlib.Topology.VectorBundle.Riemannian	1
8 files Mathlib.Analysis.Asymptotics.Completion Mathlib.Analysis.NormedSpace.Connected Mathlib.Analysis.NormedSpace.RieszLemma Mathlib.NumberTheory.TsumDivsorsAntidiagonal Mathlib.Topology.Algebra.InfiniteSum.Order Mathlib.Topology.Compactness.HilbertCubeEmbedding Mathlib.Topology.Instances.Real.Lemmas Mathlib.Topology.Semicontinuous	5

---

Declarations diff

+ CompleteLattice.hasProd
+ CompleteLattice.multipliable
+ Multipliable.tprod_union_of_disjoint
+ Summable.tsum_union_disjoint
+ le_tprod
+ le_tprod_of_mem
+ mul_tsum
+ ne_top_of_tprod_ne_top
+ prod_le_tprod
+ prod_mul_tprod_compl
+ singleton_mul_tprod_ne
+ tprod_biUnion
+ tprod_biUnion'
+ tprod_biUnion_le
+ tprod_biUnion_le_tprod
+ tprod_comm
+ tprod_comp_eq_tprod_of_bijective
+ tprod_comp_eq_tprod_of_equiv
+ tprod_comp_le_tprod_of_injective
+ tprod_eq_iSup_prod
+ tprod_eq_iSup_prod'
+ tprod_eq_mul_tprod_ite
+ tprod_eq_one_iff
+ tprod_eq_top_of_eq_top
+ tprod_fiberwise
+ tprod_iUnion_eq_tprod
+ tprod_iUnion_le
+ tprod_iUnion_le_prod
+ tprod_iUnion_le_tprod
+ tprod_image_le_tprod_comp
+ tprod_insert
+ tprod_le_of_subset
+ tprod_le_tprod
+ tprod_le_tprod_comp_of_surjective
+ tprod_mono_subtype
+ tprod_mul
+ tprod_prod
+ tprod_prod'
+ tprod_range_le_tprod_comp
+ tprod_sigma
+ tprod_sigma'
+ tprod_subtype_eq_top_of_eq_top
+ tprod_subtype_eq_tprod_mulSupport
+ tprod_top
+ tprod_union_le
+ tprod_union_of_disjoint
+ tsum_mul

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

---

No changes to strong technical debt.

No changes to weak technical debt.

[wwylele]

This is in the root namespace, which will appear first in doc search, meanwhile the more commonly applicable one Multipliable.tprod_mul is in the Multipliable namespace. I suggest we do either one of the following

• Move this to CompleteLattice as well. For consistency, maybe just do this for this entire section?
• Add a doc string to say "see also Multipliable.tprod_mul that doesn't require CompleteLattice"

[Jun2M]

I am hesitant to moving theorems to CompleteLattice namespace as it is an instance whereas Multipliable is a def which you can use dot notation with. I will try to add doc strings to places where there is more general Multipliable version.

[wwylele]

I believe the naming convention says this should be

Suggested change

	@[to_additive] theorem tprod_union_disjoint (hd : Disjoint s t) :
	@[to_additive] theorem tprod_union_of_disjoint (hd : Disjoint s t) :