[Merged by Bors] - chore(Analysis/SpecificLimits/Basic): generalize lemmas

[astrainfinita]

---

• depends on: [Merged by Bors] - chore(Topology/Algebra/Order/Field): generalize some lemmas to Semifield #28472
• depends on: [Merged by Bors] - feat: add ContinuousSMul instances for ℚ≥0 #28474
• depends on: [Merged by Bors] - chore: remove MulAction ℚ α → MulAction ℚ≥0 α instances #30671

[github-actions]

PR summary 6f6a8a0377

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Analysis.SpecificLimits.Basic	1452	1458	+6 (+0.41%)
Mathlib.Analysis.Real.Hyperreal	1457	1463	+6 (+0.41%)
Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber	1457	1463	+6 (+0.41%)
Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric	1764	1763	-1 (-0.06%)
Mathlib.Analysis.Normed.Algebra.Exponential	1799	1798	-1 (-0.06%)
Mathlib.Analysis.CStarAlgebra.Spectrum	2563	2562	-1 (-0.04%)

Import changes for all files

Files	Import difference
249 files Mathlib.Analysis.Analytic.Binomial Mathlib.Analysis.CStarAlgebra.ApproximateUnit Mathlib.Analysis.CStarAlgebra.CStarMatrix Mathlib.Analysis.CStarAlgebra.CompletelyPositiveMap Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Commute Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Integral Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Range Mathlib.Analysis.CStarAlgebra.Exponential Mathlib.Analysis.CStarAlgebra.GelfandDuality Mathlib.Analysis.CStarAlgebra.Hom Mathlib.Analysis.CStarAlgebra.Module.Constructions Mathlib.Analysis.CStarAlgebra.Module.Defs Mathlib.Analysis.CStarAlgebra.PositiveLinearMap Mathlib.Analysis.CStarAlgebra.Projection Mathlib.Analysis.CStarAlgebra.SpecialFunctions.PosPart Mathlib.Analysis.CStarAlgebra.Spectrum Mathlib.Analysis.CStarAlgebra.Unitary.Connected Mathlib.Analysis.CStarAlgebra.Unitary.Span Mathlib.Analysis.Calculus.BumpFunction.Convolution Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension Mathlib.Analysis.Calculus.BumpFunction.InnerProduct Mathlib.Analysis.Calculus.BumpFunction.SmoothApprox Mathlib.Analysis.Calculus.LineDeriv.IntegrationByParts Mathlib.Analysis.Calculus.LogDerivUniformlyOn Mathlib.Analysis.Calculus.Rademacher Mathlib.Analysis.Complex.AbsMax Mathlib.Analysis.Complex.Angle Mathlib.Analysis.Complex.CauchyIntegral Mathlib.Analysis.Complex.ExponentialBounds Mathlib.Analysis.Complex.Hadamard Mathlib.Analysis.Complex.Harmonic.Analytic Mathlib.Analysis.Complex.Harmonic.MeanValue Mathlib.Analysis.Complex.HasPrimitives Mathlib.Analysis.Complex.JensenFormula Mathlib.Analysis.Complex.Liouville Mathlib.Analysis.Complex.LocallyUniformLimit Mathlib.Analysis.Complex.MeanValue Mathlib.Analysis.Complex.OpenMapping Mathlib.Analysis.Complex.Periodic Mathlib.Analysis.Complex.PhragmenLindelof Mathlib.Analysis.Complex.Polynomial.Basic Mathlib.Analysis.Complex.Polynomial.GaussLucas Mathlib.Analysis.Complex.Polynomial.UnitTrinomial Mathlib.Analysis.Complex.Positivity Mathlib.Analysis.Complex.RemovableSingularity Mathlib.Analysis.Complex.Schwarz Mathlib.Analysis.Complex.SummableUniformlyOn Mathlib.Analysis.Complex.TaylorSeries Mathlib.Analysis.Complex.UpperHalfPlane.Exp Mathlib.Analysis.Complex.UpperHalfPlane.Manifold Mathlib.Analysis.Complex.UpperHalfPlane.Metric Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction Mathlib.Analysis.Complex.ValueDistribution.FirstMainTheorem Mathlib.Analysis.Complex.ValueDistribution.ProximityFunction Mathlib.Analysis.Convex.SpecificFunctions.Deriv Mathlib.Analysis.Distribution.AEEqOfIntegralContDiff Mathlib.Analysis.Distribution.FourierSchwartz Mathlib.Analysis.Distribution.SchwartzSpace Mathlib.Analysis.Distribution.TemperateGrowth Mathlib.Analysis.Fourier.AddCircleMulti Mathlib.Analysis.Fourier.AddCircle Mathlib.Analysis.Fourier.FourierTransformDeriv Mathlib.Analysis.Fourier.Inversion Mathlib.Analysis.Fourier.PoissonSummation Mathlib.Analysis.Fourier.ZMod Mathlib.Analysis.FunctionalSpaces.SobolevInequality Mathlib.Analysis.InnerProductSpace.Harmonic.Analytic Mathlib.Analysis.InnerProductSpace.Harmonic.Constructions Mathlib.Analysis.InnerProductSpace.NormPow Mathlib.Analysis.InnerProductSpace.StarOrder Mathlib.Analysis.Matrix.Order Mathlib.Analysis.MellinInversion Mathlib.Analysis.MellinTransform Mathlib.Analysis.Normed.Algebra.Basic Mathlib.Analysis.Normed.Algebra.DualNumber Mathlib.Analysis.Normed.Algebra.Exponential Mathlib.Analysis.Normed.Algebra.GelfandFormula Mathlib.Analysis.Normed.Algebra.GelfandMazur Mathlib.Analysis.Normed.Algebra.MatrixExponential Mathlib.Analysis.Normed.Algebra.QuaternionExponential Mathlib.Analysis.Normed.Algebra.Spectrum Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt Mathlib.Analysis.NormedSpace.DualNumber Mathlib.Analysis.ODE.Gronwall Mathlib.Analysis.ODE.PicardLindelof Mathlib.Analysis.Polynomial.Factorization Mathlib.Analysis.Polynomial.MahlerMeasure Mathlib.Analysis.Real.Pi.Bounds Mathlib.Analysis.Real.Pi.Chudnovsky Mathlib.Analysis.Real.Pi.Irrational Mathlib.Analysis.Real.Pi.Wallis Mathlib.Analysis.SpecialFunctions.Arsinh Mathlib.Analysis.SpecialFunctions.BinaryEntropy Mathlib.Analysis.SpecialFunctions.Complex.Analytic Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Isometric Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Isometric Mathlib.Analysis.SpecialFunctions.ExpDeriv Mathlib.Analysis.SpecialFunctions.Exponential Mathlib.Analysis.SpecialFunctions.Gamma.Basic Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup Mathlib.Analysis.SpecialFunctions.Gamma.Deriv Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral Mathlib.Analysis.SpecialFunctions.Gaussian.PoissonSummation Mathlib.Analysis.SpecialFunctions.ImproperIntegrals Mathlib.Analysis.SpecialFunctions.Integrability.Basic Mathlib.Analysis.SpecialFunctions.Integrability.LogMeromorphic Mathlib.Analysis.SpecialFunctions.Integrals.Basic Mathlib.Analysis.SpecialFunctions.Integrals.LogTrigonometric Mathlib.Analysis.SpecialFunctions.Integrals.PosLogEqCircleAverage Mathlib.Analysis.SpecialFunctions.JapaneseBracket Mathlib.Analysis.SpecialFunctions.Log.Deriv Mathlib.Analysis.SpecialFunctions.Log.NegMulLog Mathlib.Analysis.SpecialFunctions.MulExpNegMulSq Mathlib.Analysis.SpecialFunctions.NonIntegrable Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric Mathlib.Analysis.SpecialFunctions.PolarCoord Mathlib.Analysis.SpecialFunctions.Pow.Deriv Mathlib.Analysis.SpecialFunctions.Pow.Integral Mathlib.Analysis.SpecialFunctions.Sigmoid Mathlib.Analysis.SpecialFunctions.SmoothTransition Mathlib.Analysis.SpecialFunctions.Stirling Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds Mathlib.Analysis.SpecialFunctions.Trigonometric.ComplexDeriv Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv Mathlib.Analysis.SpecialFunctions.Trigonometric.Series Mathlib.Analysis.SpecialFunctions.Trigonometric.Sinc Mathlib.Combinatorics.Additive.AP.Three.Behrend Mathlib.Combinatorics.Derangements.Exponential Mathlib.Combinatorics.Extremal.RuzsaSzemeredi Mathlib.Combinatorics.SimpleGraph.LapMatrix Mathlib.Computability.AkraBazzi.AkraBazzi Mathlib.Computability.AkraBazzi.SumTransform Mathlib.Data.Complex.ExponentialBounds Mathlib.Data.Real.Pi.Bounds Mathlib.Data.Real.Pi.Irrational Mathlib.Data.Real.Pi.Wallis Mathlib.Geometry.Manifold.BumpFunction Mathlib.Geometry.Manifold.Complex Mathlib.Geometry.Manifold.Instances.Sphere Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique Mathlib.Geometry.Manifold.IntegralCurve.UniformTime Mathlib.Geometry.Manifold.PartitionOfUnity Mathlib.Geometry.Manifold.PoincareConjecture Mathlib.Geometry.Manifold.Riemannian.Basic Mathlib.Geometry.Manifold.Riemannian.PathELength Mathlib.Geometry.Manifold.WhitneyEmbedding Mathlib.InformationTheory.KullbackLeibler.Basic Mathlib.InformationTheory.KullbackLeibler.KLFun Mathlib.MeasureTheory.Constructions.HaarToSphere Mathlib.MeasureTheory.Function.SpecialFunctions.Sinc Mathlib.MeasureTheory.Integral.CircleAverage Mathlib.MeasureTheory.Integral.CircleIntegral Mathlib.MeasureTheory.Integral.CircleTransform Mathlib.MeasureTheory.Integral.ExpDecay Mathlib.MeasureTheory.Integral.Gamma Mathlib.MeasureTheory.Integral.IntegralEqImproper Mathlib.MeasureTheory.Integral.IntervalIntegral.TrapezoidalRule Mathlib.MeasureTheory.Integral.PeakFunction Mathlib.MeasureTheory.Integral.TorusIntegral Mathlib.MeasureTheory.Measure.Lebesgue.VolumeOfBalls Mathlib.NumberTheory.AbelSummation Mathlib.NumberTheory.Bertrand Mathlib.NumberTheory.Cyclotomic.Embeddings Mathlib.NumberTheory.Cyclotomic.PID Mathlib.NumberTheory.Cyclotomic.Three Mathlib.NumberTheory.DirichletCharacter.GaussSum Mathlib.NumberTheory.EulerProduct.ExpLog Mathlib.NumberTheory.FLT.Three Mathlib.NumberTheory.Fermat Mathlib.NumberTheory.GaussSum Mathlib.NumberTheory.Harmonic.Bounds Mathlib.NumberTheory.Harmonic.EulerMascheroni Mathlib.NumberTheory.JacobiSum.Basic Mathlib.NumberTheory.LSeries.AbstractFuncEq Mathlib.NumberTheory.LSeries.Deriv Mathlib.NumberTheory.LSeries.Positivity Mathlib.NumberTheory.LSeries.SumCoeff Mathlib.NumberTheory.LegendreSymbol.AddCharacter Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.GaussSum Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity Mathlib.NumberTheory.LucasLehmer Mathlib.NumberTheory.ModularForms.Basic Mathlib.NumberTheory.ModularForms.EisensteinSeries.Basic Mathlib.NumberTheory.ModularForms.EisensteinSeries.MDifferentiable 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.QExpansion Mathlib.NumberTheory.NumberField.AdeleRing Mathlib.NumberTheory.NumberField.CMField Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord Mathlib.NumberTheory.NumberField.ClassNumber Mathlib.NumberTheory.NumberField.Completion Mathlib.NumberTheory.NumberField.Cyclotomic.Embeddings Mathlib.NumberTheory.NumberField.Cyclotomic.PID Mathlib.NumberTheory.NumberField.Cyclotomic.Three Mathlib.NumberTheory.NumberField.DedekindZeta Mathlib.NumberTheory.NumberField.Discriminant.Basic Mathlib.NumberTheory.NumberField.Embeddings 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.Ideal 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.Transcendental.Lindemann.AnalyticalPart Mathlib.NumberTheory.ZetaValues Mathlib.Probability.Distributions.Exponential Mathlib.Probability.Distributions.Gamma Mathlib.Probability.Distributions.Pareto Mathlib.Probability.Distributions.Poisson Mathlib.RingTheory.Polynomial.Hermite.Gaussian Mathlib.RingTheory.Polynomial.Selmer Mathlib.Tactic.FunProp.ContDiff Mathlib.Tactic.FunProp.Differentiable Mathlib.Tactic.NormNum.LegendreSymbol Mathlib.Tactic Mathlib.Topology.Compactification.OnePoint.Sphere	-1
Mathlib.Data.Complex.FiniteDimensional Mathlib.LinearAlgebra.Complex.FiniteDimensional	5
84 files Mathlib.Algebra.ArithmeticGeometric Mathlib.Analysis.Asymptotics.LinearGrowth Mathlib.Analysis.BoxIntegral.Box.SubboxInduction Mathlib.Analysis.BoxIntegral.Partition.Filter Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction Mathlib.Analysis.Complex.Cardinality Mathlib.Analysis.Hofer Mathlib.Analysis.Normed.Group.Completeness Mathlib.Analysis.Normed.Group.Pointwise Mathlib.Analysis.Normed.Order.UpperLower Mathlib.Analysis.Real.Cardinality Mathlib.Analysis.Real.Hyperreal Mathlib.Analysis.SpecificLimits.ArithmeticGeometric Mathlib.Analysis.SpecificLimits.Basic Mathlib.Data.Complex.Cardinality Mathlib.Data.Real.Cardinality Mathlib.Data.Real.Hyperreal Mathlib.Dynamics.BirkhoffSum.QuasiMeasurePreserving Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber Mathlib.Dynamics.Ergodic.Ergodic Mathlib.Dynamics.Ergodic.MeasurePreserving Mathlib.MeasureTheory.Constructions.ProjectiveFamilyContent Mathlib.MeasureTheory.Constructions.Projective Mathlib.MeasureTheory.Covering.VitaliFamily Mathlib.MeasureTheory.Function.AEMeasurableSequence Mathlib.MeasureTheory.Group.Arithmetic Mathlib.MeasureTheory.Group.Defs Mathlib.MeasureTheory.Group.MeasurableEquiv Mathlib.MeasureTheory.Group.Pointwise Mathlib.MeasureTheory.Measure.AEDisjoint Mathlib.MeasureTheory.Measure.AEMeasurable Mathlib.MeasureTheory.Measure.AbsolutelyContinuous Mathlib.MeasureTheory.Measure.AddContent Mathlib.MeasureTheory.Measure.Comap Mathlib.MeasureTheory.Measure.Count Mathlib.MeasureTheory.Measure.Decomposition.Exhaustion Mathlib.MeasureTheory.Measure.Decomposition.Hahn Mathlib.MeasureTheory.Measure.Dirac Mathlib.MeasureTheory.Measure.Map Mathlib.MeasureTheory.Measure.MeasureSpaceDef Mathlib.MeasureTheory.Measure.MeasureSpace Mathlib.MeasureTheory.Measure.MutuallySingular Mathlib.MeasureTheory.Measure.NullMeasurable Mathlib.MeasureTheory.Measure.QuasiMeasurePreserving Mathlib.MeasureTheory.Measure.Real Mathlib.MeasureTheory.Measure.Restrict Mathlib.MeasureTheory.Measure.Sub Mathlib.MeasureTheory.Measure.Trim Mathlib.MeasureTheory.Measure.Typeclasses.Finite Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms Mathlib.MeasureTheory.Measure.Typeclasses.Probability Mathlib.MeasureTheory.Measure.Typeclasses.SFinite Mathlib.MeasureTheory.Measure.Typeclasses Mathlib.MeasureTheory.Measure.WithDensityFinite Mathlib.MeasureTheory.Order.Group.Lattice Mathlib.MeasureTheory.Order.Lattice Mathlib.MeasureTheory.OuterMeasure.Caratheodory Mathlib.MeasureTheory.OuterMeasure.Induced Mathlib.MeasureTheory.OuterMeasure.OfAddContent Mathlib.MeasureTheory.OuterMeasure.OfFunction Mathlib.MeasureTheory.Topology Mathlib.MeasureTheory.VectorMeasure.Basic Mathlib.MeasureTheory.VectorMeasure.Decomposition.Hahn Mathlib.MeasureTheory.VectorMeasure.Decomposition.JordanSub Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan Mathlib.Probability.ConditionalProbability Mathlib.Probability.ProbabilityMassFunction.Basic Mathlib.Probability.ProbabilityMassFunction.Binomial Mathlib.Probability.ProbabilityMassFunction.Constructions Mathlib.Probability.ProbabilityMassFunction.Monad Mathlib.Probability.UniformOn Mathlib.Topology.Baire.CompleteMetrizable Mathlib.Topology.GDelta.MetrizableSpace Mathlib.Topology.GDelta.UniformSpace Mathlib.Topology.MetricSpace.CantorScheme Mathlib.Topology.MetricSpace.Closeds Mathlib.Topology.MetricSpace.Contracting Mathlib.Topology.MetricSpace.Cover Mathlib.Topology.MetricSpace.HausdorffDistance Mathlib.Topology.MetricSpace.Perfect Mathlib.Topology.MetricSpace.PiNat Mathlib.Topology.MetricSpace.Polish Mathlib.Topology.MetricSpace.ThickenedIndicator Mathlib.Topology.MetricSpace.Thickening	6

---

Declarations diff

+ NNRat.tendsto_algebraMap_inv_atTop_nhds_zero_nat
+ NNRat.tendsto_inv_atTop_nhds_zero_nat
+ RCLike.tendsto_add_mul_div_add_mul_atTop_nhds
+ RCLike.tendsto_inverse_atTop_nhds_zero_nat
+ tendsto_algebraMap_inv_atTop_nhds_zero_nat
+ tendsto_inv_atTop_nhds_zero_nat
+-- tendsto_inverse_atTop_nhds_zero_nat

You can run this locally as follows

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

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• [Merged by Bors] - chore(Topology/Algebra/Order/Field): generalize some lemmas to Semifield #28472
• [Merged by Bors] - feat: add ContinuousSMul instances for ℚ≥0 #28474
• [Merged by Bors] - chore: remove MulAction ℚ α → MulAction ℚ≥0 α instances #30671
  By Dependent Issues (🤖). Happy coding!

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.

[j-loreaux]

This is nice, thanks for doing it!

bors merge

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

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