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CHANGELOG_UNRELEASED.md

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Changelog (unreleased)

[Unreleased]

Added

  • in realfun.v:

    • lemma derivable_sqrt

  • in classical_sets.v:

    • definition rectangle
    • lemmas rectangle_setX, setI_closed_rectangle
    • definitions cross, cross12
    • lemmas smallest_sub_sub, bigcap_closed_smallest, smallest_sub_iff
    • lemma preimage_set_systemS

  • in measurable_structure.v:

    • lemmas g_sigma_algebra_cross, g_sigma_algebra_rectangle

  • in measurable_function.v:

    • lemma preimage_measurability

Changed

  • moved from measurable_structure.v to classical_sets.v:

    • definition preimage_set_system
    • lemmas preimage_set_system0, preimage_set_systemU, preimage_set_system_comp, preimage_set_system_id

  • in functions.v:

    • lemmas linfunP, linfun_eqP
    • instances of SubLmodule and pointedType on {linear _->_ | _ }

  • in tvs.v:

    • structure LinearContinuous
    • factory isLinearContinuous
    • instance of ChoiceType on {linear_continuous _ -> _ }
    • instance of LinearContinuous with the composition of two functions of type LinearContinuous
    • instance of LinearContinuous with the sum of two functions of type LinearContinuous
    • instance of LinearContinuous with the scalar multiplication of a function of type LinearContinuous
    • instance of Continuous on -f when f is of type LinearContinuous
    • instance of SubModClosed on {linear_continuous _ -> _}
    • instance of SubLModule on {linear_continuous _ -> _ }
    • instance of LinearContinuous on the null function
    • notations {linear_continuous _ -> _ | _ } and {linear_continuous _ -> _ }
    • definitions lcfun, lcfun_key, lcfunP`
    • lemmas lcfun_eqP, null_fun_continuous, fun_cvgD, fun_cvgN, fun_cvgZ, fun_cvgZr
    • lemmas lcfun_continuous and lcfun_linear

Changed

  • in functions.v:

    • lemmas linfunP, linfun_eqP
    • instances of SubLmodule and pointedType on {linear _->_ | _ }

  • in tvs.v:

    • structure LinearContinuous

    • factory isLinearContinuous

    • instance of ChoiceType on {linear_continuous _ -> _ }

    • instance of LinearContinuous with the composition of two functions of type LinearContinuous

    • instance of LinearContinuous with the sum of two functions of type LinearContinuous

    • instance of LinearContinuous with the scalar multiplication of a function of type LinearContinuous

    • instance of Continuous on -f when f is of type LinearContinuous

    • instance of SubModClosed on {linear_continuous _ -> _}

    • instance of SubLModule on {linear_continuous _ -> _ }

    • instance of LinearContinuous on the null function

    • notations {linear_continuous _ -> _ | _ } and {linear_continuous _ -> _ }

    • definitions lcfun, lcfun_key, lcfunP`

    • lemmas lcfun_eqP, null_fun_continuous, fun_cvgD, fun_cvgN, fun_cvgZ, fun_cvgZr

    • lemmas lcfun_continuous and lcfun_linear

    • ...

  • in derive.v:

    • lemmas derivable_max, derive_maxl, derive_maxr derivable_min, derive_minl, derive_minr
    • lemmas derivable0, derive0, is_derive0

  • in topology_structure.v:

    • lemma not_limit_pointE

  • in separation_axioms.v:

    • lemmas limit_point_closed

  • in convex.v:

    • lemma convex_setW

  • in convex.v:

    • lemma convexW

Changed

  • moved from topology_structure.v to filter.v:

    • lemma continuous_comp (and generalized)

  • in set_interval.v

    • setUitv1, setU1itv, setDitv1l, setDitv1r (generalized)

  • in set_interval.v

    • itv_is_closed_unbounded (fix the definition)

  • in set_interval.v

    • itv_is_open_unbounded, itv_is_oo, itv_open_ends (Prop to bool)

  • in lebesgue_Rintegrable.v:

    • lemma Rintegral_cst (does not use cst anymore)

  • split probability.v into directory probability_theory and move contents as:

    • file probability.v:
    • file bernoulli_distribution.v:
      • definitions bernoulli_pmf, bernoulli_prob
      • lemmas bernoulli_pmf_ge0, bernoulli_pmf1, measurable_bernoulli_pmf, eq_bernoulli, bernoulli_dirac, eq_bernoulliV2, bernoulli_probE, measurable_bernoulli_prob, measurable_bernoulli_prob2
    • file beta_distribution.v:
      • lemmas continuous_onemXn, onemXn_derivable, derivable_oo_LRcontinuous_onemXnMr, derive_onemXn, Rintegral_onemXn
      • definition XMonemX
      • lemmas XMonemX_ge0, XMonemX_le1, XMonemX0n, XMonemXn0, XMonemX00, XMonemXC, XMonemXM, continuous_XMonemX, within_continuous_XMonemX, measurable_XMonemX, bounded_XMonemX, integrable_XMonemX, integrable_XMonemX_restrict, integral_XMonemX_restrict`
      • definition beta_fun
      • lemmas EFin_beta_fun, beta_fun_sym, beta_fun0n, beta_fun00, beta_fun1Sn, beta_fun11, beta_funSSnSm, beta_funSnSm, beta_fun_fact, beta_funE, beta_fun_gt0, beta_fun_ge0
      • definition beta_pdf
      • lemmas measurable_beta_pdf, beta_pdf_ge0, beta_pdf_le_beta_funV, integrable_beta_pdf, bounded_beta_pdf_01
      • definition beta_prob
      • lemmas integral_beta_pdf, beta_prob01, beta_prob_fin_num, beta_prob_dom, beta_prob_uniform, integral_beta_prob_bernoulli_prob_lty, integral_beta_prob_bernoulli_prob_onemX_lty, integral_beta_prob_bernoulli_prob_onem_lty, beta_prob_integrable, beta_prob_integrable_onem, beta_prob_integrable_dirac, beta_prob_integrable_onem_dirac, integral_beta_prob`
      • definition div_beta_fun
      • lemmas div_beta_fun_ge0, div_beta_fun_le1
      • definition beta_prob_bernoulli_prob
      • lemmas beta_prob_bernoulli_probE
    • file binomial_distribution.v:
      • definition binomial_pmf
      • lemmas measurable_binomial_pmf
      • definition binomial_prob
      • definition bin_prob
      • lemmas bin_prob0, bin_prob1, binomial_msum, binomial_probE, integral_binomial, integral_binomial_prob, measurable_binomial_prob
    • file exponential_distribution.v:
      • definition exponential_pdf
      • lemmas exponential_pdf_ge0, lt0_exponential_pdf, measurable_exponential_pdf, exponential_pdfE, in_continuous_exponential_pdf, within_continuous_exponential_pdf
      • definition exponential_prob
      • lemmas derive1_exponential_pdf, exponential_prob_itv0c, integral_exponential_pdf, integrable_exponential_pdf
    • file normal_distribution.v:
      • definition normal_fun
      • lemmas measurable_normal_fun, normal_fun_ge0, normal_fun_center`
      • definition normal_peak
      • lemmas normal_peak_ge0, normal_peak_gt0
      • definition normal_pdf
      • lemmas normal_pdfE, measurable_normal_pdf, normal_pdf_ge0, continuous_normal_pdf, normal_pdf_ub
      • definition normal_prob
      • lemmas integral_normal_pdf, integrable_normal_pdf, normal_prob_dominates
    • file poisson_distribution.v:
      • definition poisson_pmf
      • lemmas poisson_pmf_ge0, measurable_poisson_pmf
      • definition poisson_prob
      • lemma measurable_poisson_prob
    • file uniform_distribution.v:
      • definition uniform_pdf
      • lemmas uniform_pdf_ge0, measurable_uniform_pdf, integral_uniform_pdf, integral_uniform_pdf1
      • definition uniform_prob
      • lemmmas integrable_uniform_pdf, dominates_uniform_prob, integral_uniform
    • file random_variable.v:
      • definition random_variable
      • lemmas notin_range_measure, probability_range
      • definition distribution
      • lemmas probability_distribution, ge0_integral_distribution, integral_distribution
      • definition cdf
      • lemmas cdf_ge0, cdf_le1, cdf_nondecreasing, cvg_cdfy1, cvg_cdfNy0, cdf_right_continuous, cdf_lebesgue_stieltjes_id, lebesgue_stieltjes_cdf_id,
      • definition ccdf
      • lemmas cdf_ccdf_1
      • corollaries ccdf_cdf_1, ccdf_1_cdf, cdf_1_ccdf
      • lemmas ccdf_nonincreasing, cvg_ccdfy0, cvg_ccdfNy1, ccdf_right_continuous
      • definition expectation
      • lemmas expectation_def, expectation_fin_num, expectation_cst, expectation_indic, integrable_expectation, expectationZl, expectation_ge0, expectation_le, expectationD, expectationB, expectation_sum, ge0_expectation_ccdf
      • definition covariance
      • lemmas covarianceE, covarianceC, covariance_fin_num, covariance_cst_l, covariance_cst_r, covarianceZl, covarianceZr, covarianceNl, covarianceNr, covarianceNN, covarianceDl, covarianceDr, covarianceBl, covarianceBr
      • definition variance
      • lemmas varianceE, variance_fin_num, variance_ge0, variance_cst, varianceZ, varianceN, varianceD, varianceB, varianceD_cst_l, varianceD_cst_r, varianceB_cst_l, varianceB_cst_r, covariance_le
      • definition mmt_gen_fun
      • lemmas markov, chernoff, chebyshev, cantelli
      • definition discrete_random_variable
      • lemmas dRV_dom_enum
      • definitions dRV_dom, dRV_enum, enum_prob
      • lemmas distribution_dRV_enum, distribution_dRV, sum_enum_prob
      • definition pmf
      • lemmas pmf_ge0, pmf_gt0_countable, pmf_measurable, dRV_expectation, expectation_pmf

  • moved from convex.v to realfun.v

    • lemma second_derivative_convex

  • in classical_sets.v

    • lemma in_set1 (statement changed)

  • in subspace_topology.v:

    • lemmas open_subspaceP and closed_subspaceP (use exists2 instead of exists)

  • moved from filter.v to classical_sets.v:

    • definition set_system

  • moved from measurable_structure.v to classical_sets.v:

    • definitions setI_closed, setU_closed

  • moved from theories to theories/topology_theory:

    • file function_spaces.v

  • moved from theories to theories/normedtype_theory:

    • file tvs.v

  • moved from tvs.v to pseudometric_normed_Zmodule.v:

    • definitions NbhsNmodule, NbhsZmodule, PreTopologicalNmodule, PreTopologicalZmodule, PreUniformNmodule, PreUniformZmodule

  • in tvs.v, turned into Let's:

    • local lemmas standard_add_continuous, standard_scale_continuous, standard_locally_convex

  • in normed_module.v, turned into Let's:

    • local lemmas add_continuous, scale_continuous, locally_convex

  • moved from normed_module.v to pseudometric_normed_Zmodule.v and generalized from normedModType to pseudoMetricNormedZmodType

    • lemma ball_open (0 < r hypothesis also not needed anymore)
    • lemma near_shift
    • lemma cvg_comp_shift
    • lemma ball_open_nbhs

  • moved from tvs.v to convex.v

    • definition convex, renamed to convex_set
    • definition convex

Renamed

  • in tvs.v:

    • definition tvsType -> convexTvsType
    • class Tvs -> ConvexTvs
    • mixin Uniform_isTvs -> Uniform_isConvexTvs
    • factory PreTopologicalLmod_isTvs -> PreTopologicalLmod_isConvexTvs
    • section Tvs_numDomain -> ConvexTvs_numDomain
    • section Tvs_numField -> ConvexTvs_numField
    • section prod_Tvs -> prod_ConvexTvs

  • in normed_module.v

    • mixin PseudoMetricNormedZmod_Tvs_isNormedModule -> PseudoMetricNormedZmod_ConvexTvs_isNormedModule

Generalized

  • in measurable_structure.v:
    • lemma sigma_algebra_measurable (not specialized to setT anymore)

Deprecated

Removed

  • in measurable_structure.v:
    • lemmas measurable_prod_g_measurableType, measurable_prod_g_measurableTypeR

Infrastructure

Misc