Changelog

Latest releases: [1.16.0] - 2026-03-17, [1.15.0] - 2026-01-15, and [1.14.0] - 2025-11-07

[1.16.0] - 2026-03-17

Added

• in unstable.v:

  • lemmas oppr_itvNy, oppr_itvy
  • lemmas ltr_norm_bound, real_ltr_bound, real_ltrNbound, ltr_bound, ltrNbound

• in classical_sets.v

  • lemma in_set1_eq

• in functions.v:

  • lemmas fun_maxC, fun_minC, min_fun_to_max, max_fun_to_min
  • lemma addBrfctE

• in set_interval.v

  • lemmas setUitv_set2, setDitv_set2, setDitvoo, setDitvoy, setDitvNyo, setDccitv, setD_cbnd_bndy, setD_bndc_Nybnd
  • definitions itv_is_closed_unbounded, itv_is_cc, itv_closed_ends
  • lemmas opp_preimage_itvbndy, opp_preimage_itvbndbnd

• in Rstruct.v:

  • lemmas R0E and R1E
  • multirule RealsE to convert from Stdlib reals to Analysis ones

• in Rstruct_topology.v:

  • lemma RlnE

• in convex.v:

  • lemma convex_setW

• in topology_structure.v

  • lemma interiorS
  • lemma not_limit_pointE

• in order_topology.v

  • lemma itv_closed_ends_closed

• in num_topology.v:

  • lemmas cvg_dnbhs_at_right, cvg_dnbhs_at_left

• in subtype_topology.v:

  • lemma within_continuous_comp

• in separation_axioms.v:

  • lemmas limit_point_closed

• in pseudometric_normed_Zmodule.v:

  • lemmas within_continuousB, within_continuousD

• in normed_module.v:

  • lemma within_continuous_compN
  • lemma compact_has_sup

• in derive.v:

  • lemmas derivable_mxP, derive_mx
  • lemmas compact_EVT_max, compact_EVT_min, EVT_max_rV, EVT_min_rV
  • lemmas derivable_max, derive_maxl, derive_maxr derivable_min, derive_minl, derive_minr
  • lemmas derivable0, derive0, is_derive0

• in numfun.v:

  • defintions funrpos, funrneg with notations ^\+ and ^\-
  • lemmas funrpos_ge0, funrneg_ge0, funrposN, funrnegN, ge0_funrposE, ge0_funrnegE, le0_funrposE, le0_funrnegE, ge0_funrposM, ge0_funrnegM, le0_funrposM, le0_funrnegM, funrposDneg, funrposBneg, funrD_posD, funrpos_le, funrneg_le
  • lemmas funerpos, funerneg

• in measurable_structure.v:

  • definitions preimage_display, g_sigma_algebra_preimageType, g_sigma_algebra_preimage
  • notations .-preimage, .-preimage.-measurable

• in measurable_function.v:

  • lemma preimage_set_system_compS
  • lemmas lt_le_nbhsr, lt_le_nbhsl

• in measurable_realfun.v:

  • definition min_mfun
  • lemmas emeasurable_fun_itv_obnd_cbndP, emeasurable_fun_itv_bndo_bndcP, emeasurable_fun_itv_cc
  • lemmas measurable_funrpos, measurable_funrneg

• in lebesgue_measure.v:

  • lemma lebesgue_measure_unique

• in lebesgue_integral_nonneg.v:

  • lemmas lebesgue_measureN, ge0_integration_by_substitution0
  • lemma integral_setU

• in lebesgue_integrable.v:

  • lemmas integrable_funrpos, integrable_funrneg

• in random_variable.v

  • lemma pmf_ge0
  • lemmas pmf_gt0_countable, pmf_measurable
  • lemmas lebesgue_integral_pmf, cdf_measurable, ccdf_measurable, le0_expectation_cdf, expectation_cdf_ccdf

Changed

• moved from filter.v to classical_sets.v:

  • definition set_system

• in classical_sets.v

  • lemma in_set1 (statement changed)

• in set_interval.v

  • setUitv1, setU1itv, setDitv1l, setDitv1r (generalized)
  • itv_is_closed_unbounded (fix the definition)
  • itv_is_open_unbounded, itv_is_oo, itv_open_ends (Prop to bool)

• in constructive_ereal.v: fixed the infamous %E scope bug.

• moved from convex.v to realfun.v

  • lemma second_derivative_convex

• in subspace_topology.v:

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

• 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

• 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

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

  • local lemmas add_continuous, scale_continuous, locally_convex

• moved from tvs.v to convex.v

  • definition convex, renamed to convex_set

• moved from realfun.v to metric_structure.v:

  • lemma cvg_at_right_left_dnbhs and generalized to metricType R

• moved from realfun.v to num_topology.v:

  • lemma left_right_continuousP

• 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

Renamed

• in set_interval.v:

  • itv_is_ray -> itv_is_open_unbounded
  • itv_is_bd_open -> itv_is_oo

• in topology_structure.v

  • closure_subset -> closureS
  • closed_comp -> preimage_closed
  • clopen_comp -> preimage_clopen

• weak_topology.v -> initial_topology.v

  • weak_topology -> initial_topology
  • weak_continuous -> initial_continuous
  • weak_ent -> initial_ent
  • weak_ball -> initial_ball
  • weak_ballE -> initial_ballE
  • open_order_weak -> open_order_initial
  • continuous_comp_weak -> continuous_comp_initial

• in subspace_topology.v:

  • weak_subspace_open -> initial_subspace_open
  • continuousFunType -> continuousSubspaceType
  • ContinuousFun -> ContinuousSubspace

• in functions_spaces.v:

  • weak_sep_cvg -> initial_sep_cvg
  • weak_sep_nbhsE -> initial_sep_nbhsE
  • weak_sep_openE -> initial_sep_openE
  • join_product_weak -> join_product_initial

• in one_point_compactification.v:

  • one_point_compactification_weak_topology -> one_point_compactification_initial_topology

• in lebesgue_integral_nonneg.v:

  • integral_setD1_EFin -> integral_setD1

Generalized

• in convex.v:

  • definition convex_function (from a realType as domain to a convex_lmodType as domain)

• in num_topology.v:

  • lemma lt_nbhsl

• in derive.v:

  • lemmas near_eq_growth_rate, near_eq_derivable, near_eq_derive, near_eq_is_derive (one less hypothesis)

• in exp.v:

  • lemma derivable_powR

• in lebesgue_integral_nonneg.v:

  • lemmas integral_itv_bndo_bndc, integral_itv_obnd_cbnd, integral_itv_bndoo

Deprecated

• in classical_sets.v:

  • lemma mem_setT

• in lebesgue_integral_nonneg.v:

  • lemma integral_setU_EFin

Removed

• in boolp.v:

  • notation eq_exists2 (was deprecated since version 1.10.0)

• in simple_functions.v:

  • definition max_sfun

• in weak_topology.v:

  • lemmas weak_ent_filter, weak_ent_refl, weak_ent_inv, weak_ent_split, weak_ent_nbhs, weak_pseudo_metric_ball_center, weak_pseudo_metric_entourageE (now Let's in initial_topology.v)

• in measurable_realfun.v:

  • lemma max_mfun_subproof (has become a Let)

• in lebesgue_integral_nonneg.v:

  • lemma integral_setU (was deprecated since version 1.0.1)

[1.15.0] - 2026-01-15

Added

• in unstable.v:

  • definitions monotonic, strict_monotonic
  • lemma strict_monotonicW
  • notation .~ for onem

• in classical_sets.v:

  • lemma nonemptyPn
  • lemmas setUDl, setUDr

• in cardinality.v:

  • lemma infinite_setD
  • lemmas finite_setX_or, infinite_setX
  • lemmas infinite_prod_rat, ``card_rat2`
  • notation cofinite_set
  • lemmas cofinite_setT, infinite_setN0, sub_cofinite_set, sub_infinite_set, cofinite_setUl, cofinite_setUr, cofinite_setU, cofinite_setI, cofinite_set_infinite, infinite_setIl, infinite_setIr
  • lemma injective_gtn

• in topology_structure.v:

  • definition isolated
  • lemma isolatedS
  • lemma disjoint_isolated_limit_point
  • lemma closure_isolated_limit_point

• in subspace_topology.v:

  • definition from_subspace

• in order_topology.v:

  • structures POrderedNbhs, POrderedTopological, POrderedUniform, POrderedPseudoMetric, POrderedPointedTopological

• in num_topology.v:

  • lemmas continuous_rsubmx, continuous_lsubmx

• new file metric_structure.v:

  • mixin PseudoMetric_isMetric, structure Metric, type metricType
    • with fields mdist, mdist_ge0, mdist_positivity, ballEmdist
  • lemmas metric_sym, mdistxx, mdist_gt0, metric_triangle, metric_hausdorff
  • R^o declared to be an instance of metricType
  • module metricType_numDomainType
    • lemmas ball_mdistE, nbhs_nbhs_mdist, nbhs_mdistP, filter_from_mdist_nbhs, fcvgrPdist_lt, cvgrPdist_lt, cvgr_dist_lt, cvgr_dist_le, nbhsr0P, cvgrPdist_le
  • factory isMetric

• in separation_axioms.v:

  • lemma perfectP

• in reals.v:

  • lemma nat_has_minimum

• in normed_module.v:

  • lemma limit_point_infinite_setP
  • lemma open_subball_rat
  • fact isolated_rat_ball
  • lemma countable_isolated
  • lemma limit_point_setD

• in convex.v:

  • lemmas convN, conv_le

• in sequences.v:

  • lemma increasing_seq_injective
  • definition adjacent_set
  • lemmas adjacent_sup_inf, adjacent_sup_inf_unique
  • definition cut
  • lemmas cut_adjacent, infinite_bounded_limit_point_nonempty
  • lemma cluster_eventuallyP
  • lemmas cluster_eventually_cvg, limit_point_cluster_eventually
  • lemma finite_range_cst_subsequence
  • lemmas infinite_increasing_seq, infinite_increasing_seq_wf
  • lemma finite_range_cvg_subsequence
  • theorem bolzano_weierstrass

• in derive.v:

  • lemmas differentiable_rsubmx, differentiable_lsubmx

• in measurable_structure.v:

  • lemma dynkin_induction

• in measure_negligible.v:

  • definition null_set with notation _.-null_set
  • lemma subset_null_set
  • lemma negligible_null_set
  • lemma measure0_null_setP
  • lemma null_setU
  • definition null_dominates
  • lemma null_dominates_trans
  • lemma null_content_dominatesP

• in measurable_realfun.v:

  • lemma measurable_funN
  • lemmas nondecreasing_measurable, nonincreasing_measurable

• in lebesgue_integrable.v

  • lemma null_set_integrable
  • lemma integrable_set0
  • lemma integrable_norm

• in lebesgue_integral_fubini.v:

  • definition product_subprobability
  • lemma product_subprobability_setC

• new file lebesgue_integral_theory/giry.v

  • definition measure_eq
  • definition giry
  • definition giry_ev
  • definition giry_measurable
  • definition preimg_giry_ev
  • definition giry_display
  • lemma measurable_giry_ev
  • definition giry_int
  • lemmas measurable_giry_int, measurable_giry_codensity
  • definition giry_map
  • lemmas measurable_giry_map, giry_int_map, giry_map_dirac
  • definition giry_ret
  • lemmas measurable_giry_ret, giry_int_ret
  • definition giry_join
  • lemmas measurable_giry_join, sintegral_giry_join, giry_int_join
  • definition giry_bind
  • lemmas measurable_giry_bind, giry_int_bind
  • lemmas giry_joinA, giry_join_id1, giry_join_id2, giry_map_zero
  • definition giry_prod
  • lemmas measurable_giry_prod, giry_int_prod1, giry_int_prod2

• in charge.v:

  • definition charge_dominates
  • lemma charge_null_dominatesP
  • lemma content_charge_dominatesP

Changed

• in Rstruct.v:

  • lemmas RleP, RltP (change implicits)

• in subspace_topology.v:

  • notation {within _, continuous _} (now uses from_subspace)

• in pseudometric_normed_Zmodule.v:

  • factory NormedZmoduleMetric with field mdist_norm

• moved from pseudometric_normed_Zmodule.v to num_topology.v:

  • notations ^'+, ^'-
  • definitions at_left, at_right
  • instances at_right_proper_filter, at_left_proper_filter
  • lemmas nbhs_right_gt, nbhs_left_lt, nbhs_right_neq, nbhs_left_neq, nbhs_left_neq, nbhs_left_le, nbhs_right_lt, nbhs_right_ltW, nbhs_right_ltDr, nbhs_right_le, not_near_at_rightP

• in measurable_structure.v:

  • the notation `<< is now for null_set_dominates, the previous definition can be recovered with the lemma null_dominatesP

• moved from realfun.v to numfun.v:

  • notations nondecreasing_fun, nonincreasing_fun, increasing_fun, decreasing_fun
  • generalized from realType to numDomainType:
    • lemmas nondecreasing_funN, nonincreasing_funN
  • generalized from realType to porderType
    • definitions itv_partition, itv_partitionL, itv_partitionR
    • lemmas itv_partition_nil, itv_partition_cons, itv_partition1, itv_partition_size_neq0, itv_partitionxx, itv_partition_le, itv_partition_cat, itv_partition_nth_size, itv_partition_nth_ge, itv_partition_nth_le, nondecreasing_fun_itv_partition
  • generalized from realType to orderType
    • lemmas itv_partitionLP, itv_partitionRP, in_itv_partition, notin_itv_partition
  • generalize from realType to numDomainType:
    • lemmas nonincreasing_fun_itv_partition, itv_partition_rev

• moved from realfun.v to numfun.v:

  • generalize from realType to numDomainType
    • definition variation
    • lemmas variation_zip, variation_prev, variation_next, variation_nil, variation_ge0, variationN, variation_le, nondecreasing_variation, nonincreasing_variation, variation_cat (order of parameters also changed), le_variation, variation_opp_rev, variation_rev_opp
  • generalize from realType to realDomainType
    • lemmas variation_itv_partitionLR, variation_subseq

• moved from realfun.v to numfun.v:

  • generalize from realType to numDomainType
    • definition variations, bounded_variation
    • lemmas variations_variation, variations_neq0, variationsN, variationsxx
    • lemmas bounded_variationxx, bounded_variationD, bounded_variationN, bounded_variationl, bounded_variationr, variations_opp, nondecreasing_bounded_variation

• moved from realfun.v to metric_structure.v and generalized:

  • lemma cvg_nbhsP

• in lebesgue_integral_monotone_convergence.v:

  • lemma ge0_le_integral (remove superfluous hypothesis)

• in charge.v:

  • dominates_cscalel specialized from set _ -> \bar _ to {measure set _ -> \bar _}

Renamed

• in boolp.v:

  • notP -> not_notP
  • notE -> not_notE

• in measure_negligible.v:

  • measure_dominates_ae_eq -> null_dominates_ae_eq

• in probability.v:

  • derivable_oo_continuous_bnd_onemXnMr -> derivable_oo_LRcontinuous_onemXnMr

• in charge.v:

  • induced -> induced_charge

Generalized

• in num_topology.v:

  • lemma in_continuous_mksetP

• in pseudometric_normed_Zmodule.v:

  • lemmas continuous_within_itvP, continuous_within_itvcyP, continuous_within_itvNycP
  • lemma within_continuous_continuous
  • lemmas open_itvoo_subset, open_itvcc_subset, realFieldType

• in num_normedtype.v:

  • weaken hypothesis in lemmas mono_mem_image_segment, mono_surj_image_segment, inc_surj_image_segment, dec_surj_image_segment, inc_surj_image_segmentP, dec_surj_image_segmentP, mono_surj_image_segmentP

• in derive.v:

  • definition jacobian
  • lemmas deriveEjacobian, differentiable_coord

• in lebesgue_integral_under.v:

  • weaken an hypothesis of lemma continuity_under_integral

• in lebesgue_integrable.v:

  • weaken an hypothesis of lemma finite_measure_integrable_cst
  • lemma null_set_integral

• in realfun.v:

  • generalized from realType to realFieldType:
    • definition total_variation
    • lemmas total_variationxx, nondecreasing_total_variation, total_variationN

• in ftc.v:

  • lemmas parameterized_integral_continuous, integration_by_substitution_decreasing, integration_by_substitution_oppr, integration_by_substitution_increasing, integration_by_substitution_onem, Rintegration_by_substitution_onem

Deprecated

• in unstable.v:

  • notation `1-

• in topology_structure.v:

  • lemma closure_limit_point (use closure_limit_point_isolated instead)

Removed

• in unstable.v:

  • definition monotonous (use strict_monotonic instead)
  • lemma abs_ceil_ge

• in set_interval.v:

  • lemma interval_set1 (use set_itv1 instead)
  • notation subset_itvS (deprecated since 1.4.0)

• in classical_sets.v:

  • notation notin_set (deprecated since 1.2.0)
  • notations in_setM, setM0, set0M, setMTT, setMT, setTM, setMI, setM_bigcupr, setM_bigcupl, setSM, bigcupM1l, bigcupM1r, setM, setMR, setML, bigcup_setM_dep, bigcup_setM, fst_setM, snd_setM, fst_setMR, in_xsectionM, in_ysectionM, notin_xsectionM, notin_ysectionM (deprecared since 1.3.0)

• in cardinality.v:

  • notations finite_setM, fset_setM, finite_setMR, finite_setML, countableMR, countableM, countableML, infiniteMRl, cardMR_eq_nat (deprecared since 1.3.0)

• in signed.v:

  • notations num_le_maxr, num_le_maxl, num_le_minr, num_le_minl, num_lt_maxr, num_lt_maxl, num_lt_minr, num_lt_minl (deprecated since 1.2.0)

• in separation_axioms.v:

  • definition cvg_toi_locally_close (deprecated since 1.5.0)

• in pseudometric_structure.v:

  • definition cvg_toi_locally (deprecated since 1.6.0)

• in constructive_ereal.v:

  • notations gee_pmull, gee_addl, gee_addr, gte_addr, gte_addl, lte_subl_addr, lte_subl_addl, lte_subr_addr, lte_subr_addl, lee_subl_addr, lee_subl_addl, lee_subr_addr, lee_subr_addl (deprecated since 1.2.0)
  • notations gte_dopp, lte_le_add, lee_lt_add, lte_le_sub, lee_opp2, lte_opp2, lte_dadd, lee_daddl, lee_daddr gee_daddl, gee_daddr, lte_daddl, lte_daddr, gte_dsubl, gte_dsubr, gte_daddl, gte_daddr, lte_dadd2lE, lee_dadd2rE, lee_dadd2l, lee_dadd2r, lee_dadd, lee_dsub, lte_dsubl_addr, lte_dsubl_addl, lte_dsubr_addr, lte_dsubr_addl, lte_le_dadd, lee_lt_dadd, lte_le_dsub, lte_pdivr_mull, lte_pdivr_mulr, lte_pdivl_mull, lte_pdivl_mulr, lee_pdivr_mull, lee_pdivr_mulr, lee_pdivl_mull, lee_pdivl_mulr, lte_ndivr_mull, lte_ndivr_mulr, lte_ndivl_mull, lte_ndivl_mulr, lee_ndivr_mull, lee_ndivr_mulr, lee_ndivl_mull, lee_ndivl_mulr, eqe_pdivr_mull (deprecared since 1.3.0)

• in reals.v:

  • lemma le_ceil (deprecated since 1.3.0)

• in sequences.v:

  • notation eq_bigsetU_seqD(deprecated since 1.2.0)

• in realfun.v:

  • notation lime_sup_ge0 (deprecated since 1.3.0)

• in measurable_structure.v:

  • notations monotone_class, monotone_class_g_salgebra, smallest_monotone_classE, monotone_class_subset, setI_closed_gdynkin_salgebra, dynkin_g_dynkin, dynkin_monotone, salgebraType (deprecated since 1.2.0)
  • definition measure_dominates (use null_set_dominates instead)
  • lemma measure_dominates_trans
  • notation measurableM (deprecated since 1.3.0)

• in measure_function.v:

  • notations g_salgebra_measure_unique_trace, g_salgebra_measure_unique_cover, g_salgebra_measure_unique (deprecated since 1.2.0)

• in measurable_realfun.v:

  • notations measurable_fine, measurable_exprn, measurable_mulrl, measurable_mulrr, measurable_oppr, measurable_normr, measurable_fun_pow, measurable_oppe, measurable_abse, measurable_EFin, measurable_natmul (deprecated since 1.4.0)
  • notation EFin_measurable_fun (deprecated since 1.6.0)

• in lebesgue_stieltjes_measure.v:

  • notation wlength_sigma_sub_additive (deprecated since 1.1.0)

• in lebesgue_integral_nonneg.v:

  • notations integral_setI_indic, integralEindic (deprecated since 1.3.0)

• in charge.v:

  • lemma dominates_charge_variation (use charge_null_dominatesP instead)

[1.14.0] - 2025-11-07

Added

• in unstable.v:

  • lemmas coprime_prodr, Gauss_dvd_prod, expn_prod, mono_leq_infl, card_big_setU
  • lemmas leq_Mprod_prodD, leq_fact2, normr_onem

• in set_interval.v:

  • lemmas itv_setU_setT, disjoint_rays

• in constructive_ereal.v:

  • lemma ltgte_fin_num
  • lemmas mule_natr, dmule_natr
  • lemmas inve_eqy, inve_eqNy
  • variants Ione, Idummy_placeholder
  • inductives Inatmul, IEFin
  • definition parse, print
  • number notations in scopes ereal_dual_scope and ereal_scope
  • notation - 1 in scopes ereal_dual_scope and ereal_scope
  • lemma lt0_adde

• in uniform_structure.v:

  • lemma continuous_injective_withinNx

• in function_spaces.v:

  • lemmas cvg_big, continuous_big

• in pseudometric_normed_Zmodule.v:

  • lemma le0_ball0
  • lemma continuous_comp_cvg

• in num_normedtype.v:

  • lemma nbhs_infty_gtr
  • lemmas bigcup_ointsub_sup, bigcup_ointsub_mem

• in normed_module.v:

  • lemma bigcup_ointsubxx, nondisjoint_bigcup_ointsub
  • definition open_disjoint_itv
  • lemmas open_disjoint_itv_open, open_disjoint_itv_is_interval, open_disjoint_itv_trivIset, open_disjoint_itv_bigcup

• in landau.v:

  • lemma littleoE0

• in realfun.v:

  • lemma cvg_addrl_Ny
  • lemmas derivable_oy_continuous_within_itvcy, derivable_oy_continuous_within_itvNyc
  • lemmas derivable_oo_continuousW, derivable_oy_continuousWoo, derivable_oy_continuousW, derivable_Nyo_continuousWoo, derivable_Nyo_continuousW

• in derive.v:

  • lemma derive1_onem

• in exp.v:

  • lemma ln_eq0

• in ftc.v:

  • lemmas integration_by_substitution_onem, Rintegration_by_substitution_onem

• in probability.v:

  • definition ccdf
  • lemmas lebesgue_stieltjes_cdf_id, cdf_ccdf_1, ccdf_nonincreasing, cvg_ccdfy0, cvg_ccdfNy1, ccdf_right_continuous, ge0_expectation_ccdf
  • corollaries ccdf_cdf_1, ccdf_1_cdf, cdf_1_ccdf
  • lemmas continuous_onemXn, onemXn_derivable, derivable_oo_continuous_bnd_onemXnMr, derive_onemXn, Rintegral_onemXn
  • definition XMonemX
  • lemmas XMonemX_ge0, XMonemX_le1, XMonemX0n, XMonemXn0, XMonemX00, XMonemXC, XMonemXM
  • lemmas 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
  • lemmas 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
  • lemma beta_prob_bernoulli_probE

• new file pnt.v

  • definitions next_prime, prime_seq
  • lemmas leq_prime_seq, mem_prime_seq
  • theorem dvg_sum_inv_prime_seq

• new directory theories/measure_theory with new files:

  • measurable_structure.v
  • measure_function.v
  • counting_measure.v
  • dirac_measure.v
  • probability_measure.v
  • measure_negligible.v
  • measure_extension.v
  • measurable_function.v
  • measure.v

Changed

• in constructive_ereal.v:

  • instance of Monoid.isLaw for mine

• in matrix_topology.v:

  • definition mx_ball

• moved from vitali_lemma.v to pseudometric_normed_Zmodule.v and renamed:

  • closure_ball -> closure_ballE

• moved from theories/measure.v (now removed)

  • to sequences.v:
    • lemmas epsilon_trick, epsilon_trick0
  • to measure_theory/measurable_structure.v:
    • definitions setC_closed, setI_closed, setU_closed, setSD_closed, setD_closed, setY_closed, fin_bigcap_closed, finN0_bigcap_closed, fin_bigcup_closed, semi_setD_closed
    • lemma setD_semi_setD_closed
    • definitions ndseq_closed, niseq_closed, trivIset_closed, fin_trivIset_closed, setring, sigma_ring, sigma_algebra, dynkin, lambda_system, monotone
    • lemmas powerset_sigma_ring, powerset_lambda_system
    • notations <<l _, >>, <<l _ >>, <<d _ >>, <<s _, _>>, <<s _ >>, <<r _ >>, <<sr _ >>, <<M _ >>
    • lemmas lambda_system_smallest, fin_bigcup_closedP, finN0_bigcap_closedP, setD_closedP, sigma_algebra_bigcap, sigma_algebraP, smallest_sigma_algebra, sub_sigma_algebra2, sigma_algebra_id, sub_sigma_algebra, sigma_algebra0, sigma_algebraCD, sigma_algebra_bigcup, smallest_setring, sub_setring2, setring_id, sub_setring, setring0, setringD, setringU, setring_fin_bigcup, g_sigma_algebra_lambda_system, smallest_sigma_ring, sigma_ring_monotone, g_sigma_ring_monotone, sub_g_sigma_ring, setring_monotone_sigma_ring, g_monotone_monotone, g_monotone_setring, g_monotone_g_sigma_ring, monotone_setring_sub_g_sigma_ring, smallest_lambda_system, lambda_system_subset, dynkinT, dynkinC, dynkinU, dynkin_lambda_system, g_dynkin_dynkin, sigma_algebra_dynkin, dynkin_setI_sigma_algebra, setI_closed_g_dynkin_g_sigma_algebra
    • definition strace
    • lemmas subset_strace, g_sigma_ring_strace, strace_sigma_ring, setI_g_sigma_ring, sigma_algebra_strace
    • mixin isSemiRingOfSets, structure SemiRingOfSets, notation semiRingOfSetsType
    • lemma measurable_curry
    • notations .-measurable, 'measurable
    • mixin SemiRingOfSets_isRingOfSets, structure RingOfSets, notation ringOfSetsType
    • mixin RingOfSets_isAlgebraOfSets, structure AlgebraOfSets, notation algebraOfSetsType
    • mixin hasMeasurableCountableUnion
    • structure SigmaRing, structure SigmaRing, notation sigmaRingType
    • factory isSigmaRing
    • structure Measurable, notation measurableType
    • factories isRingOfSets, isRingOfSets_setY, isAlgebraOfSets, isAlgebraOfSets_setD, isMeasurable
    • lemmas bigsetU_measurable, fin_bigcup_measurable, measurableD, seqDU_measurable, measurableC, bigsetI_measurable, fin_bigcap_measurable, measurableID, bigcup_measurable, bigcap_measurable, bigcapT_measurable, countable_measurable, sigmaRingType_lambda_system, countable_bigcupT_measurable, bigcupT_measurable_rat, sigma_algebra_measurable, bigcap_measurableType
    • definition discrete_measurable
    • lemmas discrete_measurable0, discrete_measurableC, discrete_measurableU
    • definitions sigma_display, g_sigma_algebraType
    • lemmas sigma_algebraC
    • notations .-sigma, .-sigma.-measurable
    • lemma measurable_g_measurableTypeE
    • definition preimage_set_system
    • lemmas preimage_set_system0, preimage_set_systemU, preimage_set_system_comp, preimage_set_system_id, sigma_algebra_preimage
    • definition image_set_system
    • lemmas sigma_algebra_image, g_sigma_preimageE
    • definition subset_sigma_subadditive
    • lemmas big_trivIset
    • definition covered_by
    • lemmas covered_bySr, covered_byP, covered_by_finite, covered_by_countable, measurable_uncurry
    • definition g_sigma_preimageU
    • lemmas g_sigma_preimageU_comp
    • definition measure_prod_display
    • notation .-prod, .-prod.-measurable
    • lemmas measurableX, measurable_prod_measurableType, measurable_prod_g_measurableTypeR, measurable_prod_g_measurableType
    • definition g_sigma_preimage
    • lemma g_sigma_preimage_comp
    • definition measure_tuple_display
    • definition measure_dominates, notation `<<
    • lemma measure_dominates_trans
  • to measure_theory/measure_function.v:
    • definitions semi_additive2, semi_additive, semi_sigma_additive, additive2, additive, sigma_additive, subadditive, measurable_subset_sigma_subadditive
    • lemma semi_additiveW
    • lemmas semi_additiveE, semi_additive2E, additive2P
    • lemmas semi_sigma_additive_is_additive, semi_sigma_additiveE, sigma_additive_is_additive
    • mixin isContent, structure Content, notation {content set _ -> \bar _}
    • lemma content_inum_subproof
    • lemmas measure0, measure_gt0, measure_semi_additive_ord, measure_semi_additive_ord_I, content_fin_bigcup, measure_semi_additive2
    • lemmas measureU, measure_bigsetU, measure_fin_bigcup, measure_bigsetU_ord_cond, measure_bigsetU_ord, measure_fbigsetU
    • mixin Content_isMeasure
    • structure Measure, notations measure, {measure set _ -> \bar _}
    • lemma measure_inum_subproof
    • factory isMeasure, lemma eq_measure
    • lemmma measure_semi_bigcup
    • lemmas measure_sigma_additive, measure_bigcup
    • definition msum
    • definition mzero, lemma msum_mzero
    • definition measure_add, measure_addE
    • definition mscale
    • definition mseries
    • definition pushforward
    • module SetRing
    • notations .-ring, .-ring.-measurable
    • lemmas le_measure, measure_le0
    • lemmas content_subadditive, content_sub_fsum
    • lemmas content_ring_sup_sigma_additive, content_ring_sigma_additive
    • lemmas ring_sigma_subadditive, ring_semi_sigma_additive, semiring_sigma_additive
    • factory Content_SigmaSubAdditive_isMeasure
    • lemma measure_sigma_subadditive
    • lemma measure_sigma_subadditive_tail
    • definition fin_num_fun
    • lemmas fin_num_fun_lty, lty_fin_num_fun
    • definitions sfinite_measure, sigma_finite
    • lemma fin_num_fun_sigma_finite
    • definition mrestr
    • lemma sfinite_measure_sigma_finite
    • mixin isSFinite, structure SFiniteMeasure, notation {sfinite_measure set _ -> \bar _}
    • mixin isSigmaFinite, structure SigmaFiniteContent, notation sigma_finite_content, {sigma_finite_content set _ -> \bar _}
    • structure SigmaFiniteMeasure, notations sigma_finite_measure, {sigma_finite_measure set _ -> \bar _}
    • factory Measure_isSigmaFinite
    • lemmas sigma_finite_mzero, sfinite_mzero
    • mixin isFinite, structures FinNumFun, FiniteMeasure, notation {finite_measure set _ -> \bar _}
    • factories Measure_isFinite, Measure_isSFinite
    • definition sfinite_measure_seq
    • lemma sfinite_measure_seqP
    • definition mfrestr
    • lemmas measureIl, measureIr, subset_measure0
    • lemmas measureDI, measureD, measureU2
    • lemmas measureUfinr, measureUfinl, null_set_setU, measureU0
    • lemma eq_measureU
    • lemma g_sigma_algebra_measure_unique_trace
    • lemmas nondecreasing_cvg_mu, nonincreasing_cvg_mu
    • definition lim_sup_set
    • lemmas lim_sup_set_ub, lim_sup_set_cvg
    • lemma lim_sup_set_cvg0
    • theorem Boole_inequality
    • lemma sigma_finiteP
    • theorem generalized_Boole_inequality
    • lemmas g_sigma_algebra_measure_unique_cover, g_sigma_algebra_measure_unique
    • lemma measure_unique
  • to measure_theory/counting_measure.v:
    • definition counting
    • lemma sigma_finite_counting
  • to measure_theory/dirac_measure.v:
    • definition dirac, notation \d_
    • lemmas finite_card_sum, finite_card_dirac, infinite_card_dirac
  • to measure_theory/probability_measure.v:
    • mixin isSubProbability, structure SubProbability, notation subprobability
    • factory Measure_isSubProbability
    • mixin isProbability, structure Probability, notation probability
    • lemmas probability_le1, probability_setC
    • factory Measure_isProbability
    • definition mnormalize
    • lemmas mnormalize_id
    • definitions mset, pset, pprobability
    • lemmas lt0_mset, gt1_mset
  • to measure_theory/measure_negligible.v:
    • definition negligible, notation .-negligible
    • lemmas negligibleP, negligible_set0, measure_negligible, negligibleS, negligibleI
    • definition measure_is_complete
    • lemmas negligibleU, negligible_bigsetU, negligible_bigcup
    • definition almost_everywhere, ae_filter_ringOfSetsType, ae_properfilter_algebraOfSetsType
    • definition ae_eq, notations {ae _, _}, \forall _ \ae _, _, _ = _ [%ae _ in _], _ = _ %[ae _]
    • lemmas measure0_ae, aeW
    • instance ae_eq_equiv
    • instances comp_ae_eq, comp_ae_eq2, comp_ae_eq2', sub_ae_eq2
    • lemmas ae_eq0, ae_eq_refl, ae_eq_comp, ae_eq_comp2, ae_eq_funeposneg, ae_eq_sym, ae_eq_trans, ae_eq_sub, ae_eq_mul2r, ae_eq_mul2l, ae_eq_mul1l, ae_eq_abse, ae_foralln
    • lemmas ae_eq_subset, ae_eqe_mul2l
    • lemma measure_dominates_ae_eq
  • to measure_theory/measure_extension.v:
    • definitions sigma_subadditive, subset_sigma_subadditive
    • mixin isOuterMeasure, structure OuterMeasure
    • notation {outer_measure set _ -> \bar _}
    • factory isSubsetOuterMeasure
    • lemmas outer_measure_sigma_subadditive_tail, outer_measure_subadditive, outer_measureU2, le_outer_measureIC
    • definition caratheodory_measurable, notation .-caratheodory
    • lemma le_caratheodory_measurable
    • lemmas outer_measure_bigcup_lim, caratheodory_measurable_set0, caratheodory_measurable_setC, caratheodory_measurable_setU_le, caratheodory_measurable_setU, caratheodory_measurable_bigsetU, caratheodory_measurable_setI, caratheodory_measurable_setD, disjoint_caratheodoryIU, caratheodory_additive, caratheodory_lime_le, caratheodory_measurable_trivIset_bigcup, caratheodory_measurable_bigcup
    • definition caratheodory_type, notation .-cara.-measurable
    • definition caratheodory_display, notation .-cara
    • lemmas caratheodory_measure0, caratheodory_measure_ge0, caratheodory_measure_sigma_additive, measure_is_complete_caratheodory
    • definition measurable_cover, lemmas cover_measurable, cover_subset
    • definition mu_ext, notation ^*
    • lemmas le_mu_ext, mu_ext_ge0, mu_ext0, mu_ext_sigma_subadditive
    • lemmas Rmu_ext, measurable_mu_extE, measurable_Rmu_extE
    • lemma sub_caratheodory
    • definition measure_extension
    • lemmas measure_extension_sigma_finite, measure_extension_unique
    • lemma caratheodory_measurable_mu_ext
    • definition completed_measure_extension
    • lemma completed_measure_extension_sigma_finite
  • to measure_theory/measurable_function.v:
    • mixin isMeasurableFun, structure MeasurableFun, notations {mfun _ >-> _}, [mfun of _]
    • lemmas measurable_funP, measurable_funPTI
    • definitions mfun, mfun_key, canonical mfun_keyed
    • lemmas measurable_id, measurable_comp, eq_measurable_fun, measurable_fun_eqP, measurable_cst, measurable_fun_bigcup, measurable_funU, measurable_funS, measurable_fun_if, measurable_fun_set0, measurable_fun_set1
    • definitions mfun_Sub_subproof, mfun_Sub
    • lemmas mfun_rect, mfun_val, mfuneqP
    • lemmas measurableT_comp, measurable_funTS, measurable_restrict, measurable_restrictT, measurable_fun_ifT, measurable_fun_bool, measurable_and, measurable_neg, measurable_or
    • lemmas preimage_set_system_measurable_fun, measurability
    • lemmas measurable_fun_pairP, measurable_fun_pair
    • lemmas measurable_fst, measurable_snd, measurable_swap
    • lemmas measurable_tnth, measurable_fun_tnthP, measurable_cons
    • lemmas measurable_behead, measurable_fun_if_pair
    • lemmas pair1_measurable, pair2_measurable
    • lemmas measurable_xsection, measurable_ysection, measurable_fun_pair1, measurable_fun_pair2

• in lebesgue_stieltjes_measure.v specialized from numFieldType to realFieldType:

  • lemma nondecreasing_right_continuousP
  • definition CumulativeBounded

• in lebesgue_stieltjes_measure.v, according to generalization of Cumulative, modified:

  • lemmas wlength_ge0, cumulative_content_sub_fsum, wlength_sigma_subadditive, lebesgue_stieltjes_measure_unique
  • definitions lebesgue_stieltjes_measure, completed_lebesgue_stieltjes_measure

• in probability.v:

  • definition poisson_pmf, lemmas poisson_pmf_ge0, measurable_poisson_pmf,
  • definition poisson_prob

Renamed

• in reals.v:

  • sup_le_ub -> ge_sub
  • le_inf -> inf_le
  • le_sup -> sup_le
  • sup_ubound -> ub_le_sup
  • inf_lbound -> ge_inf
  • ub_ereal_sup -> ge_ereal_sup
  • ereal_inf_le -> ge_ereal_inf
  • le_ereal_sup -> ereal_sup_le
  • le_ereal_inf -> ereal_inf_le_tmp
  • lb_ereal_inf -> le_ereal_inf_tmp
  • ereal_sup_ge -> le_ereal_sup_tmp

• in sequences.v:

  • adjacent -> adjacent_seq

• in realfun.v:

  • derivable_oo_continuous_bnd -> derivable_oo_LRcontinuous
  • derivable_oo_continuous_bnd_within -> derivable_oo_LRcontinuous_within
  • derivable_Nyo_continuous_bnd -> derivable_Nyo_Lcontinuous
  • derivable_oy_continuous_bnd -> derivable_oy_Rcontinuous
  • derivable_oy_continuous_within_itvcy -> derivable_oy_Rcontinuous_within_itvcy

• in probability.v:

  • bernoulli -> bernoulli_prob
  • bernoulli_probE -> bernoulliE
  • integral_bernoulli_prob -> integral_bernoulli_prob
  • measurable_bernoulli -> measurable_bernoulli_prob
  • measurable_bernoulli2 -> measurable_bernoulli_prob2

Generalized

• in unstable.v:

  • generalized from numDomainType to pzRingType:
    • definition onem, lemmas onme0, onem1, add_onemK, onemD, onemMr, onemM

• in set_interval.v:

  • lemma set_itv_splitI (generalized from orderType to porderType)
  • lemma disjoint_itvxx (generalized from numDomainType to porderType)
  • lemma disjoint_neitv (generalized from realFieldType to orderType)

• in pseudometric_normed_Zmodule.v:

  • lemma closed_ball0 (realFieldType -> pseudoMetricNormedZmodType)
  • lemmas closed_ball_closed, subset_closed_ball (realFieldType -> numDomainType)
  • lemma subset_closure_half (realFieldType -> numFieldType)
  • lemma le_closed_ball (pseudoMetricNormedZmodType -> pseudoMetricType)

• in matrix_normedtype.v:

  • lemmas rV_compact, mx_norm_ball, bounded_closed_compact, mx_normZ
  • example matrix_triangle

• in lebesgue_stieltjes_measure.v generalized (codomain is now an orderNbhsType):

  • lemma right_continuousW
  • record isCumulative
  • definition Cumulative

• in probabilitity.v:

  • lemma exponential_pdf_ge0 (hypothesis generalized)

Removed

• file interval_inference.v (now in MathComp)

• in reals.v:

  • notation sup_ub (was deprecated since 1.3.0)
  • notation inf_lb (was deprecated since 1.3.0)
  • notation ereal_sup_ub (was deprecated since 1.3.0)
  • notation ereal_inf_lb (was deprecated since 1.3.0)

• in file all_reals.v

  • export of interval_inference (now in mathcomp-algebra, but not automatically exported)

• in ereal.v:

  • notation ereal_sup_le (was deprecated since 1.11.0)

• file theories/measure.v

  • notations [measure of _], [measure of _]
  • notations [content of _], [content of _]
  • notations [outer_measure of _], [outer_measure of _]

[1.13.0] - 2025-08-16

Added

• in unstable.v:

  • lemma sqrtK

• in mathcomp_extra.v:

  • lemmas subrKC, sumr_le0, card_fset_sum1

• in functions.v:

  • lemmas fct_prodE, prodrfctE

• in classical_orders.v:

  • lemma big_lexi_order_prefix_closed_itv

• in topology_structure.v:

  • lemmas denseI, dense0

• in pseudometric_normed_Zmodule.v:

  • lemma dense_set1C

• in constructive_ereal.v:

  • lemma expe0, mule0n, muleS

• in reals.v:

  • definition irrational
  • lemmas irrationalE, rationalP

• new file borel_hierarchy.v:

  • definitions Gdelta, Fsigma
  • lemmas closed_Fsigma, Gdelta_measurable, Gdelta_subspace_open, irrational_Gdelta, not_rational_Gdelta

• in realfun.v:

  • instance is_derive1_sqrt

• in exp.v:

  • lemma norm_expR
  • lemmas expeR_eqy
  • lemmas lt0_powR1, powR_eq1
  • definition lne
  • lemmas le0_lneNy, lne_EFin, expeRK, lneK, lneK_eq, lne1, lneM, lne_inj, lneV, lne_div, lte_lne, lee_lne, lneXn, le_lne1Dx, lne_sublinear, lne_ge0, lne_lt0, lne_gt0, lne_le0
  • lemma lne_eq0

• in lebesgue_measure.v:

  • lemma countable_lebesgue_measure0

• in charge.v:

  • definition copp, lemma cscaleN1

• in hoelder.v

  • lemma hoelder_conj_ge1

Changed

• in constructive_ereal.v:

  • lemma mulN1e

• moved from pi_irrational.v to reals.v and changed

  • definition rational

• in measurable_realfun.v:

  • generalized and renamed:
    • measurable_fun_itv_bndo_bndc -> measurable_fun_itv_bndo_bndcP
    • measurable_fun_itv_obnd_cbnd -> measurable_fun_itv_obnd_cbndP

• moved from simple_functions.v to measure.v

  • notations {mfun _ >-> _}, [mfun of _]
  • mixin isMeasurableFun, structure MesurableFun, lemmas measurable_funP
  • definitions mfun, mfun_key, canonical mfun_keyed
  • definitions mfun_Sub_subproof, mfun_Sub
  • lemmas mfun_rect, mfun_valP, mfuneqP
  • lemma measurableT_comp_subproof

• moved from simple_functions.v to measure.v and renamed:

  • lemma measurable_sfunP -> measurable_funPTI

• moved from simple_functions.v to measurable_realfun.v

  • lemmas mfun_subring_closed, mfun0, mfun1, mfunN, mfunD, mfunB, mfunM, mfunMn, mfun_sum, mfun_prod, mfunX
  • definitions mindic, indic_mfun, scale_mfun, max_mfun
  • lemmas mindicE, max_mfun_subproof

• moved from simple_functions.v to lebesgue_stieltjes_measure.v and renamed:

  • lemma measurable_sfun_inP -> measurable_funP1

Renamed

• in derive.v:

  • derivemxE -> deriveEjacobian

• in exp.v:

  • ltr_expeR -> lte_expeR
  • ler_expeR -> lee_expeR

• in lebesgue_stieltjes_measure.v:

  • cumulativeNy0 -> cumulativeNy
  • cumulativey1 -> cumulativey

• measurable_sfunP -> measurable_funPTI (and moved from from simple_functions.v to measure.v)

• measurable_sfun_inP -> measurable_funP1 (and moved from simple_functions.v to lebesgue_stieltjes_measure.v)

Generalized

• in functions.v
  • lemma fct_sumE (from a pointwise equality to a functional one)

Removed

• file forms.v (superseded by MathComp's sesquilinear.v)

• in unstable.v:

  • dependent_choice_Type (use Rocq's dependent_choice instead)

• in simple_functions.v:

  • duplicated hints about measurable_set1
  • lemma measurableT_comp_subproof turned into a Let (now in measure.v)

[1.12.0] - 2025-07-03

Added

• in unstable.v:

  • lemma subrKC

• in classical_sets.v:

  • lemma bigcup_mkord_ord

• in set_interval.v:

  • lemma memB_itv, memB_itv0

• in constructive_ereal.v:

  • inve a total involutive inversion function on \bar R, denoted ^-1 in the ereal_scope coinciding with x^-1%R when x != 0 but such that 0^-1 = +oo and -oo^-1 = -oo,
  • notation x / y in ereal_scope for x / y = x * y^-1,
  • lemmas inver, inveP, fine_invr, inve0, inve1, invey, invey, inveNy, inveK, invr_inj, inveN, inve_eq0, inve_ge0, inve_gt0, inv_gt0P, inve_lt0, inve_le0, inve_le0P,
  • predicate inveM_def with notation x *^-1? y defining a sufficient condition for the inverse and product to commute, with lemmas inveMP, inveM_defE, inveM and fin_inveM_def,
  • compatibility lemma mule_defE to bridge the former definition of mule_def with the new one.
  • lemma fin_numV
  • lemmas mulVe, lee_pV2, lte_pV2, ltee_pV2, inve_pge, inve_pgt, inve_ple, inve_plt, inve_gt1, inve_ge1.
  • lemmas div1e, divee, inve_eq1, Nyconjugate
  • lemmas abse_prod

• in real_interval.v:

  • lemma itvNybndEbigcup

• in num_topology.v:

  • topologicalType instance on R^o for R : numDomainType

• in convex.v:

  • definition convex_quasi_associative
    • implemented through a module ConvexQuasiAssoc containing law and helper lemmas
  • lemmas convR_itv, convR_line_path

• in tvs.v:

  • HB classes TopologicalNmodule, TopologicalZmodule, TopologicalLmodule UniformNmodule, UniformZmodule, UniformLmodule
  • notation topologicalZmodType
  • mixin PreTopologicalNmodule_isTopologicalNmodule, TopologicalNmodule_isTopologicalZmodule, TopologicalZmodule_isTopologicalLmodule, PreUniformNmodule_isUniformNmodule, UniformNmodule_isUniformZmodule, PreUniformLmodule_isUniformLmodule
  • structure topologicalLmodule
  • factories PreTopologicalNmodule_isTopologicalZmodule, TopologicalNmodule_isTopologicalLmodule, PreUniformNmodule_isUniformZmodule, UniformNmodule_isUniformLmodule
  • lemmas sub_continuous, sub_unif_continuous

• in num_normedtype.v:

  • lemmas gt0_cvgMrNy, gt0_cvgMry

• in normed_module.v:

  • definition pseudoMetric_normed
  • factory Lmodule_isNormed

• in sequences.v:

  • lemma subset_seqDU

• in esum.v:

  • lemma nneseries_esumT

• in exp.v:

  • lemma expR_ge1Dxn

• in measure.v:

  • definition g_sigma_preimage
  • lemma g_sigma_preimage_comp
  • definition measure_tuple_display
  • lemma measurable_tnth
  • lemma measurable_fun_tnthP
  • lemma measurable_cons
  • lemma measurable_behead
  • lemmas seqDU_measurable, measure_gt0
  • notations \forall x \ae mu, P, f = g %[ae mu in D], f = g %[ae mu]
  • instances ae_eq_equiv, comp_ae_eq, comp_ae_eq2, comp_ae_eq2', sub_ae_eq2
  • lemma ae_eq_comp2
  • lemma ae_foralln
  • lemma ae_eqe_mul2l

• in lebesgue_stieltjes_measure.v:

  • mixin isCumulativeBounded, structure CumulativeBounded with type cumulative_bounded

• in simple_functions.v:

  • lemma mfunMn

• in lebesgue_integral_definition.v:

  • lemmas le_measure_sintegral, ge0_le_measure_integral

• in lebesgue_integral_nonneg.v:

  • lemmas ge0_nondecreasing_set_nondecreasing_integral, ge0_nondecreasing_set_cvg_integral, le0_nondecreasing_set_nonincreasing_integral, le0_nondecreasing_set_cvg_integral
  • lemma ge0_integral_ereal_sup (was a Let)

• in lebesgue_integrable.v:

  • lemma integral_sum

• in lebesgue_integral_fubini.v:

  • lemmas integral21_prod_meas2, integral12_prod_meas2

• in lebesgue_integral_differentiation.v:

  • lemma nicely_shrinking_fin_num

• new file ess_sup_inf.v:

  • lemma measure0_ae
  • definition ess_esup
  • lemmas ess_supEae, ae_le_measureP, ess_supEmu0, ess_sup_ge, ess_supP, le_ess_sup, eq_ess_sup, ess_sup_cst, ess_sup_ae_cst, ess_sup_gee, abs_sup_eq0_ae_eq, abs_ess_sup_eq0, ess_sup_pZl, ess_supZl, ess_sup_eqNyP, ess_supD, ess_sup_absD
  • notation ess_supr
  • lemmas ess_supr_bounded, ess_sup_eqr0_ae_eq, ess_suprZl, ess_sup_ger, ess_sup_ler, ess_sup_cstr, ess_suprD, ess_sup_normD
  • definition ess_inf
  • lemmas ess_infEae, ess_infEN, ess_supEN, ess_infN, ess_supN, ess_infP, ess_inf_le, le_ess_inf, eq_ess_inf, ess_inf_cst, ess_inf_ae_cst, ess_inf_gee, ess_inf_pZl, ess_infZl, ess_inf_eqyP, ess_infD
  • notation ess_infr
  • lemmas ess_infr_bounded, ess_infrZl, ess_inf_ger, ess_inf_ler, ess_inf_cstr

• in hoelder.v:

  • lemmas Lnorm_abse, Lfun_norm
  • lemmas Lnorm0, Lnorm_cst1
  • definition hoelder_conjugate
  • lemmas hoelder_conjugate0, hoelder_conjugate1, hoelder_conjugate2, hoelder_conjugatey, hoelder_conjugateK
  • lemmas lerB_DLnorm, lerB_LnormD, eminkowski
  • definition finite_norm
  • mixin isLfunction with field Lfunction_finite
  • structure Lfunction
  • notation LfunType
  • notation {mfun_ mu , U >-> V }
  • definition ae_eq_op
  • lemmas ae_eq_op_refl, ae_eq_op_sym, ae_eq_op_trans, aeEqMfun
  • canonical ae_eq_op_canonical
  • definition LspaceType
  • lemma ae_eqP
  • definition/coercion aqEqMfun_to_fun
  • definition Lspace with notation mu.-Lspace p
  • lemma Lfun_integrable, Lfun1_integrable, Lfun2_integrable_sqr, Lfun2_mul_Lfun1
  • lemma Lfun_scale, Lfun_cst,
  • definitions finLfun, Lfun, Lfun_key
  • canonical Lfun_keyed
  • lemmas sub_Lfun_mfun, sub_Lfun_finLfun
  • definition Lfun_Sub
  • lemmas Lfun_rect, Lfun_valP, LfuneqP, finite_norm_cst0, mfunP, LfunP, mfun_scaler_closed
  • lemmas LnormZ, Lfun_submod_closed
  • lemmas finite_norm_fine, ler_LnormD, LnormrN, fine_Lnormr_eq0
  • lemma fine_Lnormr_eq0
  • lemma Lfun_subset, Lfun_subset12
  • lemma Lfun_oppr_closed
  • lemma Lfun_addr_closed
  • lemmas poweR_Lnorm, oppe_Lnorm
  • lemmas hoelder_conjugate_div, hoelder_div_conjugate, hoelder_Mconjugate, hoelder_conjugateP, hoelder_conjugate_eq1, hoelder_conjugate_eqNy, hoelder_conjugate_eqy, hoelder_conjugateNy

• in probability.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
  • Definition poisson_pmf, poisson_prob
  • lemmas poisson_pmf_ge0, measurable_poisson_pmf, measurable_poisson_prob
  • instance poisson_prob
  • lemma cdf_lebesgue_stieltjes_id

Changed

• in constructive_ereal.v:

  • mule has special cases optimizing computation for +oo and -oo
  • mule_def has been rewritten to optimize computation in several cases.

• in convex.v:

  • convex combination operator a <| t |> b changed from (1-t)a + tb to ta + (1-t)b
  • definition convex_realDomainType generalized and renamed accordingly convex_numDomainType

• in sequences.v:

  • change the implicit arguments of lemma is_cvg_series_exp_coeff

• in tvs.v:

  • HB class UniformZmodule now contains TopologicalZmodule
  • HB class UniformLmodule now contains TopologicalLmodule

• in measure.v:

  • definition pushforward (to take a function instead of a proof)
  • change the implicit arguments of lemma measurability
  • notation {ae mu, P} (near use {near _, _} notation)
  • definition ae_eq
  • ae_eq lemmas now for ringType-valued functions (instead of \bar R)

• in lebesgue_integral_nonneg.v:

  • lemma integral_abs_eq0 (remove redundant hypotheses)

• in lebesgue_integral_differentiation.v:

  • definition iavg (to use inve)

• in measure.v:

  • fourth argument of probability_setT is now explicit

• moved from measurable_realfun.v to lebesgue_stieltjes_measure.v:

  • definitions measurableTypeR, measurableR
  • lemmas measurable_set1, measurable_itv

• in measure.v:

  • definition ess_sup moved to ess_sup_inf.v

Renamed

• in convex.v:

  • lemma conv_gt0 to convR_gt0

• in tvs.v:

  • HB class TopologicalNmodule moved to PreTopologicalNmodule
  • HB class TopologicalZmodule moved to PreTopologicalZmodule
  • HB class TopologicalLmodule moved to PreTopologicalLmodule
  • structure topologicalLmodule moved to preTopologicalLmodule
  • HB class UniformNmodule moved to PreUniformNmodule
  • HB class UniformZmodule moved to PreUniformZmodule
  • HB class UniformLmodule moved to PreUniformLmodule

• in normed_module.v:

  • cvgZl -> cvgZr_tmp
  • is_cvgZl -> is_cvgZr_tmp
  • cvgZr -> cvgZl_tmp
  • is_cvgZr -> is_cvgZl_tmp
  • is_cvgZrE -> is_cvgZlE
  • cvgMl -> cvgMr_tmp
  • cvgMr -> cvgMl_tmp
  • is_cvgMr -> is_cvgMl_tmp
  • is_cvgMrE -> is_cvgMlE_tmp
  • is_cvgMl -> is_cvgMr_tmp
  • is_cvgMlE -> is_cvgMrE_tmp
  • limZl -> limZr_tmp
  • limZr -> limZl_tmp
  • continuousZr -> continuousZl_tmp
  • continuousZl -> continuousZr_tmp

• in realfun.v:

  • variationD -> variation_cat

• in lebesgue_integral_fubini.v:

  • fubini1 -> integral12_prod_meas1
  • fubini2 -> integral21_prod_meas1

• in lebesgue_integrable.v:

  • integral_fune_lt_pinfty -> integrable_lty
  • integral_fune_fin_num -> integrable_fin_num

• in hoelder.v:

  • minkowski -> minkowski_EFin

Generalized

• in convex.v:

  • parameter R of convType from realDomainType to numDomainType

• in derive.v:

  • derive_cst, derive1_cst
  • lemmas is_deriveX, deriveX, exp_derive, exp_derive1

• in lebesgue_integrable.v:

  • lemma integrable_sum

• in hoelder.v:

  • definition Lnorm generalized to functions with codomain \bar R (this impacts the notation 'N_p[f])
  • lemmas Lnorm1, eq_Lnorm, Lnorm_counting (from f : _ -> R to f : _ -> \bar R)

• in probability.v:

  • lemma cantelli
  • lemmas expectation_fin_num, expectationZl, expectationD, expectationB, expectation_sum, covarianceE, covariance_fin_num, covarianceZl, covarianceZr, covarianceNl, covarianceNr, covarianceNN, covarianceDl, covarianceDr, covarianceBl, covarianceBr, varianceE, variance_fin_num, varianceZ, varianceN, varianceD, varianceB, varianceD_cst_l, varianceD_cst_r, varianceB_cst_l, varianceB_cst_r, covariance_le

Deprecated

• in set_interval.v:
  • lemma mem_1B_itvcc

Removed

• in constructive_ereal.v:

  • notations lee_addl, lee_addr, lee_add2l, lee_add2r, lee_add, lee_sub, lee_add2lE, lee_oppl, lee_oppr, lte_oppl, lte_oppr, lte_add, lte_add2lE, lte_addl, lte_addr (deprecated since 1.1.0)

• in exp.v:

  • notation expRMm (deprecated since 1.1.0)

• in measure.v:

  • definition almost_everywhere_notation
  • lemma ess_sup_ge0
  • notations sub_additive, sigma_sub_additive, content_sub_additive, ring_sigma_sub_additive, Content_SubSigmaAdditive_isMeasure.Build, measure_sigma_sub_additive, measure_sigma_sub_additive_tail, Measure_isSFinite_subdef.Build, sfinite_measure_subdef, @SigmaFinite_isFinite.Build, FiniteMeasure_isSubProbability.Build (deprecated since 1.1.0)

[1.11.0] - 2025-05-02

Added

• in unstable.v:

  • lemmas eq_exists2l, eq_exists2r
  • module ProperNotations with notations ++>, ==>, ~~>

• in mathcomp_extra.v:

  • lemmas inr_inj, inl_inj

• in boolp.v:

  • lemmas orW, or3W, or4W

• in classical_sets.v:

  • lemmas in_set1, inr_in_set_inr, inl_in_set_inr, mem_image, mem_range, image_f
  • lemmas inr_in_set_inl, inl_in_set_inl
  • lemmas set_cst, image_nonempty

• in functions.v:

  • lemma natmulfctE

• in constructive_ereal.v:

  • lemma EFin_bigmax
  • lemmas expe_ge0, expe_eq0, expe_gt0

• in ereal.v:

  • lemmas ereal_infEN, ereal_supN, ereal_infN, ereal_supEN
  • lemmas ereal_supP, ereal_infP, ereal_sup_gtP, ereal_inf_ltP, ereal_inf_leP, ereal_sup_geP, lb_ereal_infNy_adherent, ereal_sup_real, ereal_inf_real
  • lemmas ereal_sup_cst, ereal_inf_cst, ereal_sup_pZl, ereal_supZl, ereal_inf_pZl, ereal_infZl

• in sequences.v:

  • lemmas ereal_inf_seq, ereal_sup_seq

• in realfun.v:

  • lemma cvge_ninftyP

• in exp.v:

  • lemma poweRE
  • lemmas lnNy, powR_cvg0, derivable_powR, powR_derive1
  • Instance is_derive1_powR

• in measure.v:

  • lemmas mnormalize_id, measurable_fun_eqP

• in lebesgue_integral_approximation.v (now measurable_fun_approximation.v):

  • lemma measurable_prod
  • lemma measurable_fun_lte
  • lemma measurable_fun_lee
  • lemma measurable_fun_eqe
  • lemma measurable_poweR

• in ftc.v:

  • lemma integrable_locally

• in probability.v:

  • lemmas eq_bernoulli, eq_bernoulliV2

Changed

• in pi_irrational:
  • definition rational

Renamed

• in kernel.v:

  • isFiniteTransition -> isFiniteTransitionKernel

• in ereal.v:

  • ereal_sup_le -> ereal_sup_ge

• in pseudometric_normed_Zmodule.v:

  • opp_continuous -> oppr_continuous

• in lebesgue_integral_approximation.v (now measurable_fun_approximation.v):

  • emeasurable_fun_lt -> measurable_lte
  • emeasurable_fun_le -> measurable_lee
  • emeasurable_fun_eq -> measurable_lee
  • emeasurable_fun_neq -> measurable_neqe

• file lebesgue_integral_approximation.v -> measurable_fun_approximation.v

Generalized

• in functions.v:

  • fct_sumE, addrfctE, sumrfctE (from zmodType to nmodType)
  • scalerfctE (from pointedType to Type)

• in normedtype.v:

  • lemmas gt0_cvgMlNy, gt0_cvgMly

• in measurable_realfun.v

  • lemma measurable_ln

Removed

• in functions.v:

  • definitions fct_ringMixin, fct_ringMixin (was only used in an HB.instance)

• in constructive_ereal.v:

  • notations esum_ninftyP, esum_ninfty, esum_pinftyP, esum_pinfty (deprecated since 0.6.0)

• in pseudometric_structure.v:

  • notations cvg_ballPpos, app_cvg_locally (deprecated since 0.6.0)

• in product_topology.v:

  • notation compact_setM (deprecated since 0.6.0)

• in separation_axioms.v:

  • notations cvg_map_lim, cvgi_map_lim (deprecated since 0.6.6)

• in sequences.v:

  • notation nonincreasing_cvg_ge (deprecated since 0.6.6)
  • notation nondecreasing_cvg_le (deprecated since 0.6.6)
  • notations nonincreasing_cvg, nondecreasing_cvg, nonincreasing_is_cvg, nondecreasing_is_cvg, nondecreasing_dvg_lt, near_nondecreasing_is_cvg, near_nonincreasing_is_cvg (deprecated since 0.6.6)
  • notation ereal_nondecreasing_opp (deprecated since 0.6.6)
  • notations ereal_nondecreasing_cvg, ereal_nondecreasing_is_cvg, ereal_nonincreasing_cvg, ereal_nonincreasing_is_cvg (deprecated since 0.6.6)
  • notations lim_sup, lim_inf, lim_infN, lim_supE, lim_infE, lim_inf_le_lim_sup, cvg_lim_infE, cvg_lim_supE, le_lim_supD, le_lim_infD, lim_supD, lim_infD
  • notations lim_einf_shift, lim_esup_le_cvg, lim_einfN, lim_esupN, lim_einf_sup, cvgNy_lim_einf_sup, cvg_lim_einf_sup, is_cvg_lim_einfE, is_cvg_lim_esupE

• in exp.v:

  • notation gt0_ler_powR (deprecated since 0.6.5)

• in measure.v:

  • notation measurable_fun_ext (deprecated since 0.6.2)
  • notations measurable_fun_id, measurable_fun_cst, measurable_fun_comp (deprecated since 0.6.3)
  • notation measurable_funT_comp (deprecated since 0.6.3)

• in measurable_realfun.v:

  • notation measurable_fun_ln (deprecated since 0.6.3)
  • notations emeasurable_itv_bnd_pinfty, emeasurable_itv_ninfty_bnd (deprecated since 0.6.2)
  • notation measurable_fun_lim_sup (deprecated since 0.6.6)
  • notation measurable_fun_max (deprecated since 0.6.3)
  • notation measurable_fun_er_map (deprecated since 0.6.3)
  • notations emeasurable_funN, emeasurable_fun_max, emeasurable_fun_min, emeasurable_fun_funepos, emeasurable_fun_funeneg (deprecated since 0.6.3)
  • notation measurable_fun_lim_esup (deprecated since 0.6.6)

• in lebesgue_integral_nonneg.v:

  • notations ge0_integralM_EFin, ge0_integralM, integralM_indic, integralM_indic_nnsfun (deprecated since 0.6.4)

• in lebesgue_integrable.v:

  • notation integralM (deprecated since 0.6.4)

[1.10.0] - 2025-04-21

Added

• in interval_inference.v:

  • definitions IntItv.exprz, Instances.natmul_itv
  • lemmas Instances.num_spec_exprz, Instances.nat_spec_factorial
  • canonical instance Instances.exprz_inum, Instances.factorial_inum

• new file internal_Eqdep_dec.v (don't use, internal, to be removed)

• in mathcomp_extra.v:

  • lemmas exprz_ge0 and exprz_gt0
  • lemmas intrN, real_floor_itv, real_ge_floor, real_ceil_itv
  • lemmas truncn_le, real_truncnS_gt, truncn_ge_nat, truncn_gt_nat, truncn_lt_nat, real_truncn_le_nat, truncn_eq, le_truncn, real_floorD1_gt, real_floor_ge_int_tmp, real_floor_ge_int, real_floor_lt_int, le_floor, real_floor_eq, real_floor_ge0, floor_lt0, real_floor_le0, floor_gt0, floor_neq0, real_ceil_le_int_tmp, real_ceil_le_int, real_ceil_gt_int, real_ceil_eq, le_ceil_tmp, real_ceil_ge0, ceil_lt0, real_ceil_le0, ceil_gt0, ceil_neq0, truncS_gt, truncn_le_nat, floorD1_gt, floor_ge_int_tmp, floor_lt_int, floor_eq, floor_ge0, floor_le0, ceil_le_int, ceil_le_int_tmp, ceil_gt_int, ceil_eq, ceil_ge0, ceil_le0, natr_int

• in set_interval.v:

  • lemma subset_itv

• in Rstruct.v:

  • lemma Pos_to_natE (from mathcomp_extra.v)
  • lemmas RabsE, RdistE, sum_f_R0E, factE

• in Rstruct_topology.v:

  • lemma RexpE

• in constructive_ereal.v:

  • definition iter_mule
  • lemma prodEFin
  • lemmas EFin_fin_numP, EFin_bigmax

• in real_interval.v:

  • lemma itvNycEbigcap

• in sequences.v:

  • lemmas nneseriesD1, geometric_ge0

• in derive.v:

  • lemmas derive_shift, is_derive_shift
  • lemma near_eq_growth_rate
  • lemmas derive1Mr, derive1Ml
  • lemmas ger0_derive1_le, ger0_derive1_le_cc, ger0_derive1_le_co, ger0_derive1_le_oc, ger0_derive1_le_oo
  • lemmas gtr0_derive1_lt, gtr0_derive1_lt_cc, gtr0_derive1_lt_co, gtr0_derive1_lt_oc, gtr0_derive1_lt_oo
  • lemmas ler0_derive1_le, ler0_derive1_le_cc, ler0_derive1_le_co, ler0_derive1_le_oc, ler0_derive1_le_oo
  • lemmas ltr0_derive1_lt, ltr0_derive1_lt_cc, ltr0_derive1_lt_co, ltr0_derive1_lt_oc, ltr0_derive1_lt_oo

• in exp.v:

  • lemma expR_sum
  • lemmas expR_le1, num_spec_expR, num_spec_powR
  • definitions expR_itv_boundl, expR_itv_boundr, expR_itv, powR_itv
  • canonical instance expR_inum, powR_inum

• in trigo.v:

  • lemma integral0oo_atan
  • lemmas num_spec_sin, num_spec_cos
  • canonical instances sin_inum, cos_inum

• new directory normedtype_theory (that replaces normedtype.v) with new files:

  • complete_normed_module.v
  • num_normedtype.v
  • ereal_normedtype.v
  • pseudometric_normed_Zmodule.v
  • matrix_normedtype.v
  • urysohn.v
  • normed_module.v
  • vitali_lemma.v
  • normedtype.v

• in normed_module.v (new file):

  • lemma near0Z

• in numfun.v:

  • lemma num_spec_indic
  • canonical instance indic_inum
  • lemmas indicC, indic_bigcup
  • lemma bounded_indic

• in measure.v:

  • lemmas preimage_set_system0, preimage_set_systemU, preimage_set_system_comp
  • lemma preimage_set_system_id
  • lemmas measurable_fun_pair1, measurable_fun_pair2

• in realfun.v:

  • lemmas cvge_pinftyP, nonincreasing_cvge

• new directory lebesgue_integral_theory with new files:

  • simple_functions.v
  • lebesgue_integral_definition.v
  • lebesgue_integral_approximation.v
  • lebesgue_integral_monotone_convergence.v
  • lebesgue_integral_nonneg.v
  • lebesgue_integrable.v
  • lebesgue_integral_dominated_convergence.v
  • lebesgue_integral_under.v
  • lebesgue_Rintegral.v
  • lebesgue_integral_fubini.v
  • lebesgue_integral_differentiation.v
  • lebesgue_integral.v

• in lebesgue_integral_approximation.v (new file):

  • lemma measurable_fun_le

• in lebesgue_Rintegral.v (new file):

  • lemma RintegralD

• in lebesgue_integrable.v (new file):

  • lemma integrable_indic_itv

• in lebesgue_integral_dominated_convergence.v (new file):

  • lemma dominated_cvg (was previously Local)

• in ftc.v:

  • lemma continuity_under_integral

• in kernel.v:

  • mixin isSigmaFiniteTransitionKernel, structure SigmaFiniteTransitionKernel, notations sigma_finite_kernel, R .-sigmafker X ~> Y
  • mixin isFiniteTransition, structure FiniteTransitionKernel, notations finite_transition_kernel, R .-ftker X ~> Y
  • lemmas sprob_kernelP, sprob_kernel_le1
  • definition kfcomp, lemmas kfcompk1, kfcompkindic, measurable_kfcomp
  • definitions kproduct, kproduct_snd
  • lemmas measurable_kproduct, semi_sigma_additive_kproduct
  • definition mkproduct
  • theorem sigma_finite_mkproduct
  • definition kcomp_noparam
  • lemma kcomp_noparamE
  • definition mkcomp_noparam
  • theorem sprob_mkcomp_noparam

• in probability.v:

  • definition cdf
  • lemmas cdf_ge0, cdf_le1, cdf_nondecreasing, cvg_cdfy1, cvg_cdfNy0, cdf_right_continuous
  • definitions normal_fun, normal_peak
  • lemmas measurable_normal_fun, normal_fun_ge0, normal_fun_center
  • lemmas normal_peak_ge0, normal_peak_gt0
  • lemma normal_pdfE
  • lemma normal_pdf_ge0, normal_pdf_ub
  • lemma integrable_normal_pdf

Changed

• in interval_inference.v:

  • definition IntItv.exprn_le1_bound
  • lemmas Instances.nat_spec_succ, Instances.num_spec_natmul, Instances.num_spec_intmul, Instances.num_itv_bound_exprn_le1
  • canonical instance Instances.succn_inum

• file nsatz_realtype.v moved from reals to reals-stdlib package

• in classical_sets.v:

  • change implicit arguments of subsetT

• topology.v now exports separation_axioms

• file separation_axioms.v moved from theories to theories/topology_theory

• moved from normedtype.v (old file) to num_topology.v

  • lemmas nbhsN, cvg_compNP, nbhsNimage, nearN, openN, closedN, dnbhsN, closure_sup, right_bounded_interior, left_bounded_interior, withinN

• the contents of normedtype.v (old file) can be found in the files in directory normed_theory unless stated otherwise

• in filter.v:

  • change implicit arguments of cvg_comp

• moved from gauss_integral to trigo.v:

  • oneDsqr, oneDsqr_ge1, oneDsqr_inum, oneDsqrV_le1, continuous_oneDsqr, continuous_oneDsqr

• moved, generalized, and renamed from gauss_integral to trigo.v:

  • integral01_oneDsqr -> integral0_oneDsqr

• in lebesgue_Rintegral.v (new file):

  • le_normr_integral renamed to le_normr_Rintegral

• moved to lebesgue_measure.v (from old lebesgue_integral.v)

  • compact_finite_measure

• moved from ftc.v to lebesgue_integral_under.v (new file):

  • notation 'd1, definition partial1of2, lemmas partial1of2E, cvg_differentiation_under_integral, differentiation_under_integral, derivable_under_integral

• in probability.v:

  • definition normal_pdf changed to use normal_fun and normal_peak

Renamed

• in mathcomp_extra.v

  • comparable_min_le_min -> comparable_le_min2
  • comparable_max_le_max -> comparable_le_max2
  • min_le_min -> le_min2
  • max_le_max -> le_max2
  • real_sqrtC -> sqrtC_real

• in boolp.v:

  • eq_fun2 -> eq2_fun
  • eq_fun3 -> eq3_fun
  • eq_forall2 -> eq2_forall
  • eq_forall3 -> eq3_forall

• in set_interval.v:

  • set_itv_infty_infty -> set_itvNyy
  • set_itv_o_infty -> set_itvoy
  • set_itv_c_infty -> set_itvcy
  • set_itv_infty_o -> set_itvNyo
  • set_itv_infty_c -> set_itvNyc
  • set_itv_pinfty_bnd -> set_itv_ybnd
  • set_itv_bnd_ninfty -> set_itv_bndNy

• in real_interval.v:

  • itv_c_inftyEbigcap -> itvcyEbigcap
  • itv_bnd_inftyEbigcup -> itvbndyEbigcup
  • itv_o_inftyEbigcup -> itvoyEbigcup

• in normed_module.v (new file):

  • cvgeMl -> cvgeZl
  • is_cvgeMl -> is_cvgeZl
  • cvgeMr -> cvgeZr
  • is_cvgeMr -> is_cvgeZr

• in measure.v:

  • measurable_fun_prod -> measurable_fun_pair
  • prod_measurable_funP -> measurable_fun_pairP
  • measurable_pair1 -> pair1_measurable
  • measurable_pair2 -> pair2_measurable

• in lebesgue_integral_fubini.v (new file):

  • fubini1a -> integrable12ltyP
  • fubini1b -> integrable21ltyP

• in simple_functions.v (new file):

  • measurable_funP -> measurable_funPT (field of isMeasurableFun mixin)

• in kernel.v:

  • Kernel_isSFinite_subdef -> isSFiniteKernel_subdef
  • SFiniteKernel_isFinite -> isMeasureFamUub
  • FiniteKernel_isSubProbability -> isSubProbabilityKernel
  • SubProbability_isProbability -> isProbabilityKernel

Generalized

• in constructive_ereal.v:

  • lemma EFin_natmul

• in real_interval.v:

  • lemmas bigcup_itvT, itv_bndy_bigcup_BRight, itv_bndy_bigcup_BLeft_shift

• in sequences.v:

  • lemma nneseries_recl genralized with a filtering predicate P

• in pseudometric_normed_Zmodule.v (new file):

  • generalized from normedModType to pseudoMetricNormedZmodType:
    • lemmas cvgr_norm_lty, cvgr_norm_ley, cvgr_norm_gtNy, cvgr_norm_geNy, cvg_bounded

• in num_normedtype.v (new file):

  • lemmas gt0_cvgMlNy, gt0_cvgMly

• in ereal_normedtype.v (new file):

  • lower_semicontinuous, lower_semicontinuousP generalized from realType to numFieldType

• in lebesgue_integral.v

  • lemmas measurable_funP, ge0_integral_pushforward, integrable_pushforward, integral_pushforward

Deprecated

• in normedtype.v (old file):

  • pseudoMetricNormedZModType_hausdorff (use norm_hausdorff instead)

• in derive.v:

  • ler0_derive1_nincr (use ler0_derive1_le_cc instead)
  • gtr0_derive1_incr (use gtr0_le_derive1 instead)

Removed

• file mathcomp_extra.v

  • lemma Pos_to_natE (moved to Rstruct.v)
  • lemma deg_le2_ge0 (available as deg_le2_poly_ge0 in ssrnum.v since MathComp 2.1.0)
  • definitions monotonous, boxed, onem, inv_fun, bound_side, swap, prodA, prodAr, map_pair, sigT_fun (moved to new file unstable.v that shouldn't be used outside of Analysis)
  • notations `1 - r, f \^-1 (moved to new file unstable.v that shouldn't be used outside of Analysis)
  • lemmas dependent_choice_Type, maxr_absE, minr_absE, le_bigmax_seq, bigmax_sup_seq, leq_ltn_expn, last_filterP, path_lt_filter0, path_lt_filterT, path_lt_head, path_lt_last_filter, path_lt_le_last, sumr_le0, fset_nat_maximum, image_nat_maximum, card_fset_sum1, onem0, onem1, onemK, add_onemK, onem_gt0, onem_ge0, onem_le1, onem_lt1, onemX_ge0, onemX_lt1, onemD, onemMr, onemM, onemV, lez_abs2, ler_gtP, ler_ltP, real_ltr_distlC, prodAK, prodArK, swapK, lt_min_lt, intrD1, intr1D, floor_lt_int, floor_ge0, floor_le0, floor_lt0, floor_eq, floor_neq0, ceil_gt_int, ceil_ge0, ceil_gt0, ceil_le0, abs_ceil_ge, nat_int, bij_forall, and_prop_in, mem_inc_segment, mem_dec_segment, partition_disjoint_bigfcup, partition_disjoint_bigfcup, prodr_ile1, size_filter_gt0, ltr_sum, ltr_sum_nat (moved to new file unstable.v that shouldn't be used outside of Analysis)

• in classical_sets.v:

  • notations setvI, setIv, bigcup_set, bigcup_set_cond, bigcap_set, bigcap_set_cond

• in filter.v:

  • definition at_point (redundant with principal_filter)

• in reals.v:

  • lemmas floor_le, le_floor (deprecated since 1.3.0)

• in measure.v:

  • notations measurable_fun_fst, measurable_fun_snd, measurable_fun_swap (deprecated since 0.6.3)

• file lebesgue_integral.v (split in several files in the directory lebesgue_integral_theory)

• file normedtype.v (split in several files in the directory normed_theory)

[1.9.0] - 2025-02-20

Added

• in mathcomp_extra.v:

  • lemmas prodr_ile1, nat_int
  • lemmas size_filter_gt0, ltr_sum, ltr_sum_nat
  • lemmas comparable_BSide_min, BSide_min, BSide_max, real_BSide_min, real_BSide_max, natr_min, natr_max, comparable_min_le_min, comparable_max, min_le_min, max_le_max and real_sqrtC

• in classical_sets.v:

  • lemmas xsectionE, ysectionE
  • lemma itv_sub_in2

• in interval_inference.v

  • definitions Itv.t, Itv.sub, Itv.num_sem, Itv.nat_sem, Itv.real1, Itv.real2, TypInstances.real_domain_typ, TypInstances.real_field_typ, TypInstances.nat_typ, ItvNum, ItvReal and Itv01
  • definitions IntItv.min, IntItv.max, Instances.min_max_typ, Instances.min_typ_inum, Instances.max_typ_inum, Instances.num_min_max_typ, Instances.natmul_inum, Instances.intmul_inum, IntItv.keep_pos_bound, IntItv.keep_neg_bound, Instances.inv_inum, IntItv.exprn_le1_bound, IntItv.exprn, Instances.exprn_inum, Instances.norm_inum, Instances.sqrt_itv, Instances.sqrt_inum, Instances.sqrtC_itv, Instances.sqrtC_inum, Instances.zero_inum, Instances.succn_inum, Instances.addn_inum, Instances.double_inum, Instances.muln_inum, Instances.expn_inum, Instances.minn_inum, Instances.maxn_inum, Instances.nat_min_max_typ, Instances.Posz_inum, Instances.Negz_inum, IntItv.keep_nonneg_bound, IntItv.keep_nonpos_bound, IntItv.keep_sign, IntItv.keep_nonpos, IntItv.keep_nonneg
  • lemmas Itv.spec_real1, Itv.spec_real2, TypInstances.real_domain_typ_spec, TypInstances.real_field_typ_spec, TypInstances.nat_typ_spec, top_wider_anything, real_wider_anyreal, le_num_itv_bound, num_itv_bound_le_BLeft, BRight_le_num_itv_bound, num_spec_sub, cmp0, neq0, eq0F, map_itv_bound_comp, map_itv_comp, inum_min, inum_max, num_le_max, num_ge_max, num_le_min, num_ge_min, num_lt_max, num_gt_max, num_lt_min, num_gt_min, itvnum_subdef, itvreal_subdef, itv01_subdef
  • lemmas Instances.num_spec_min, Instances.num_spec_max, Instances.nat_num_spec, Instances.num_spec_natmul, Instances.num_spec_int, Instances.num_spec_intmul, Instances.num_itv_bound_keep_pos, Instances.num_itv_bound_keep_neg, Instances.num_spec_inv, Instances.num_itv_bound_exprn, Instances.num_spec_exprn, Instances.num_spec_norm, num_abs_le, num_abs_lt, Instances.num_spec_sqrt, Instances.num_spec_sqrtC, Instances.nat_spec_zero, Instances.nat_spec_succ, Instances.nat_spec_add, Instances.nat_spec_double, Instances.nat_spec_mul, Instances.nat_spec_exp, Instances.nat_spec_min, Instances.nat_spec_max, Instances.num_spec_Posz, Instances.num_spec_Negz
  • notation %:num
  • notations {posnum R}, {nonneg R}, %:pos, %:nng, %:posnum, %:nngnum, [gt0 of _], [lt0 of _], [ge0 of _], [le0 of _], [cmp0 of _], [neq0 of _]
  • definitions PosNum, NngNum, posnum_spec and nonneg_spec
  • lemmas posnumP and nonnegP
  • definitions ItvReal and Itv01
  • lemmas cmp0, neq0, eq0F, num_min, num_max
  • notation %:num
  • notations {posnum R}, {nonneg R}, %:pos, %:nng, %:posnum, %:nngnum, [gt0 of _], [lt0 of _], [ge0 of _], [le0 of _], [cmp0 of _], [neq0 of _]
  • definitions PosNum and NngNum

• in constructive_ereal.v:

  • lemma abse_EFin
  • lemmas cmp0y, cmp0Ny, real_miney, real_minNye, real_maxey, real_maxNye, oppe_cmp0, real_fine, real_muleN, real_mulNe, real_muleNN
  • definition ext_num_sem
  • lemmas ext_num_num_sem, ext_num_num_spec, le_map_itv_bound_EFin, map_itv_bound_EFin_le_BLeft, BRight_le_map_itv_bound_EFin, le_ext_num_itv_bound, ext_num_spec_sub
  • definition ext_widen_itv
  • lemmas gt0e, lte0, ge0e, lee0, cmp0e, neqe0
  • lemmas ext_num_spec_pinfty
  • canonicals pinfty_inum, oppe_inum, EFin_inum, fine_inum, oppe_inum, adde_inum, dEFin_inum, dadde_inum
  • lemmas ext_num_spec_ninfty, ext_num_spec_EFin, num_spec_fine, ext_num_sem_y, ext_num_sem_Ny, oppe_boundr, oppe_boundl, ext_num_spec_opp, ext_num_spec_add, ext_num_spec_dEFin, ext_num_spec_dadd
  • variant ext_sign_spec
  • lemmas ext_signP, ext_num_itv_mul_boundl, ext_num_itv_mul_boundr_pos, ext_num_itv_mul_boundr, comparable_ext_num_itv_bound, ext_num_itv_bound_min, ext_num_itv_bound_max, ext_num_spec_mul
  • canonicals mule_inum, abse_inum, ext_min_max_typ
  • definition abse_itv
  • lemmas ext_num_spec_abse, ext_min_itv_boundr_spec, ext_num_spec_min, ext_max_itv_boundl_spec, ext_max_itv_boundr_spec, ext_num_spec_max

• in set_interval.v:

  • lemma set_itv_splitU

• in ereal.v:

  • lemmas ext_num_spec_ereal_sup, ext_num_spec_ereal_inf
  • canonicals ereal_sup_inum, ereal_inf_inum

• in topology_theory/topological_structure.v

  • lemmas interior_id, interiorT, interior0, closureT

• in topology_theory/num_topology.v:

  • lemmas lt_nbhsl, Nlt_nbhsl
  • lemma lt_nbhsr

• in normedtype.v:

  • lemma scaler1
  • lemma nbhs_right_leftP
  • lemmas bounded_cst, subr_cvg0
  • lemma cvgr_expr2, cvgr_idn
  • lemmas ninfty, cvgy_compNP
  • global hint to automatically apply interval_open
  • lemmas cvg_compNP, decreasing_itvNyo_bigcup, decreasing_itvoo_bigcup, increasing_itvNyo_bigcup, increasing_itvoc_bigcup
  • lemmas gt0_cvgMlNy, gt0_cvgMly

• in sequences.v:

  • lemma seqDUE
  • lemma nondecreasing_telescope_sumey

• in derive.v:

  • lemmas horner0_ext, hornerD_ext, horner_scale_ext, hornerC_ext, derivable_horner, derivE, continuous_horner
  • instance is_derive_poly
  • lemmas decr_derive1_le0, decr_derive1_le0_itv, decr_derive1_le0_itvy, decr_derive1_le0_itvNy, incr_derive1_ge0, incr_derive1_ge0_itv, incr_derive1_ge0_itvy, incr_derive1_ge0_itvNy,
  • lemmas ler0_derive1_nincry, ger0_derive1_ndecry, ler0_derive1_nincrNy, ger0_derive1_ndecrNy
  • lemmas ltr0_derive1_decr, gtr0_derive1_incr
  • lemmas near_eq_derivable, near_eq_derive, near_eq_is_derive
  • lemmas derive1N, derivable_opp, derive1_id

• in real_interval.v:

  • lemma itv_bnd_infty_bigcup0S
  • lemma itv_bndy_bigcup_BLeft_shift

• in numfun.v

  • lemmas funeposE, funenegE, funepos_comp, funeneg_comp

• in trigo.v:

  • lemma derivable_atan

• in realfun.v:

  • definition discontinuity
  • lemmas nondecreasing_fun_sum_le, discontinuty_countable
  • definitions derivable_Nyo_continuous_bnd, derivable_oy_continuous_bnd
  • lemma cvg_addrr_Ny
  • lemmas lhopital_at_left, lhopital_at_left, lhopital,

• new file measurable_realfun.v

  • with as contents the first half of the file lebesgue_measure.v
  • lemmas measurable_fun_itv_bndo_bndc, measurable_fun_itv_obnd_cbnd

• in lebesgue_integral.v:

  • lemmas integral_fin_num_abs, Rintegral_cst, le_Rintegral
  • lemma integral_bigsetU_EFin
  • lemmas interior_itv_bnd, interior_itv_bndy, interior_itv_Nybnd, definition interior_itv
  • lemma interior_set1
  • lemmas interior_itv_bnd, interior_itv_bndy, interior_itv_Nybnd, interior_itv_Nyy
  • definition interior_itv
  • lemma RintegralB
  • lemma ge0_cvgn_integral

• in ftc.v:

  • lemmas differentiation_under_integral, derivable_under_integral
  • definition partial1of2, lemma partial1of2E
  • lemma ge0_continuous_FTC2y
  • lemma Rintegral_ge0_continuous_FTC2y
  • lemma le0_continuous_FTC2y
  • lemmas decreasing_ge0_integration_by_substitutiony, ge0_integration_by_substitutionNy, increasing_ge0_integration_by_substitutiony, ge0_integration_by_substitutionNy, increasing_ge0_integration_by_substitutionT, ge0_symfun_integralT

• in probability.v:

  • definition normal_pdf
  • lemmas normal_pdf_ge0, normal_pdf_gt0, measurable_normal_pdf, continuous_normal_pdf, normal_pdf_ub
  • definition normal_prob, equipped with the structure of probability measure
  • lemmas integral_normal_pdf, normal_prob_dominates

• new file pi_irrational.v:

  • lemmas measurable_poly
  • definition rational
  • module pi_irrational
  • lemma pi_irrationnal

• new file gauss_integral.v:

  • definition oneDsqr
  • lemmas oneDsqr_gt0, oneDsqr_ge0, oneDsqr_ge1, oneDsqr_neq0, oneDsqrV_le1, continuous_oneDsqr, continuous_oneDsqrV, integral01_oneDsqr
  • canonical oneDsqr_ge0_snum
  • definition gauss_fun
  • lemmas gauss_fun_ge0, gauss_le1, cvg_gauss_fun, measurable_gauss_fun, continuous_gauss_fun
  • module gauss_integral_proof
  • lemma integral0y_gauss
  • lemmas integralT_gauss, integrableT_gauss

Changed

• in Rstruct.v

  • instantiate GRinv.inv by Rinv instead of Rinvx

• file interval_inference.v

  • definitions Itv.def, Itv.spec, Itv.typ, empty_itv

• moved from topology_structure.v to discrete_topology.v: discrete_open, discrete_set1, discrete_closed, and discrete_cvg.

• in cantor.v, cantor_space now defined in terms of bool

• moved from pseudometric_structure.v to discrete_topology.v: discrete_ent, discrete_ball, and discrete_topology.

• in separation_axioms.v, updated discrete_hausdorff, and discrete_zero_dimension to take a discreteTopologicalType

• moved from normedtype.v to num_topology.v and renamed:

  • nbhs_lt -> lt_nbhsl_lt
  • nbhs_le -> lt_nbhsl_le

• in normedtype.v:

  • lemma cvgyNP renamed to cvgNy_compN and generalized

• in numfun.v

  • lock funepos, funeneg

• in derive.v:

  • put the notation ^`() and ^`( _ ) in scope classical_set_scope

• in measure.v:

  • content_snum -> content_inum
  • measure_snum -> measure_inum

• file lebesgue_measure.v

  • first half moved to a new file measurable_realfun.v

• moved from lebesgue_integral.v to measure.v and generalized

  • lemmas measurable_xsection, measurable_ysection

• in lebesgue_integral.v

  • change implicits of measurable_funP

Renamed

• file itv.v to interval_inference.v

• in interval_inference.v

  • opp_itv_bound_subdef -> IntItv.opp_bound
  • opp_itv_bound_subdef -> IntItv.opp_bound
  • opp_itv_ge0_subproof -> IntItv.opp_bound_ge0
  • opp_itv_gt0_subproof -> IntItv.opp_bound_gt0
  • opp_itv_subdef -> IntItv.opp
  • add_itv_boundl_subdef -> IntItv.add_boundl
  • add_itv_boundr_subdef -> IntItv.add_boundr
  • add_itv_subdef -> IntItv.add
  • itv_bound_signl -> IntItv.sign_boundl
  • itv_bound_signr -> IntItv.sign_boundr
  • interval_sign -> IntItv.sign
  • interval_sign -> IntItv.sign
  • mul_itv_boundl_subdef -> IntItv.mul_boundl
  • mul_itv_boundr_subdef -> IntItv.mul_boundr
  • mul_itv_boundrC_subproof -> IntItv.mul_boundrC
  • mul_itv_subdef -> IntItv.mul
  • Itv.top_typ_subproof -> TypInstances.top_typ_spec
  • itv_top_typ -> TypInstances.itv_top_typ
  • typ_inum_subproof -> TypInstances.typ_inum_spec
  • typ_inum -> TypInstances.typ_inum
  • zero_inum -> Instances.zero_inum
  • one_inum -> Instances.one_inum
  • opp_itv_boundl_subproof -> Instances.one_boundl
  • opp_itv_boundr_subproof -> Instances.one_boundr
  • opp_inum_subproof -> Instances.num_spec_opp
  • opp_inum -> Instances.opp_inum
  • add_inum_subproof -> Instances.num_spec_add
  • add_inum -> Instances.add_inum
  • interval_sign_spec -> Instances.sign_spec
  • interval_signP -> Instances.signP
  • mul_itv_boundl_subproof -> Instances.num_itv_mul_boundl
  • mul_itv_boundr_subproof -> Instances.num_itv_mul_boundr
  • mul_itv_boundr'_subproof -> Instances.BRight_le_mul_boundr
  • map_itv_bound_min -> Instances.num_itv_bound_min
  • map_itv_bound_max -> Instances.num_itv_bound_max
  • mul_inum_subproof -> Instances.num_spec_mul
  • mul_inum -> Instances.mul_inum
  • itv_bottom -> bottom
  • itv_gt0 -> gt0
  • itv_le0F -> le0F
  • itv_lt0 -> lt0
  • itv_ge0F -> ge0F
  • itv_ge0 -> ge0
  • itv_lt0F -> lt0F
  • itv_le0 -> le0
  • itv_gt0F -> gt0F
  • itv_top_typ -> top_typ
  • Itv.map_itv_bound -> map_itv_bound
  • Itv.map_itv -> map_itv
  • inum_eq -> num_eq
  • inum_le -> num_le
  • inum_lt -> num_lt
  • inum_min -> num_min
  • inum_max -> num_max

• in set_interval.v:

  • opp_itv_bnd_infty -> opp_itv_bndy
  • opp_itv_infty_bnd -> opp_itvNy_bnd

• in real_interval.v:

  • itv_bnd_infty_bigcup -> itv_bndy_bigcup_BRight
  • itv_bnd_infty_bigcup0S -> itv0y_bigcup0S
  • itv_infty_bnd_bigcup -> itvNy_bnd_bigcup_BLeft

• in normedtype.v:

  • cvge_sub0 -> sube_cvg0

• in measure.v

  • preimage_class -> preimage_set_system
  • image_class -> image_set_system
  • preimage_classes -> g_sigma_preimageU
  • preimage_class_measurable_fun -> preimage_set_system_measurable_fun
  • sigma_algebra_preimage_class -> sigma_algebra_preimage
  • sigma_algebra_image_class -> sigma_algebra_image
  • sigma_algebra_preimage_classE -> g_sigma_preimageE
  • preimage_classes_comp -> g_sigma_preimageU_comp
  • setDI_closed -> setD_closed
  • setDI_semi_setD_closed -> setD_semi_setD_closed
  • sedDI_closedP -> setD_closedP
  • setringDI -> setringD

• in lebesgue_integral.v:

  • Rintegral_setU_EFin -> Rintegral_setU

Generalized

• in Rstruct.v:

  • lemma RsqrtE

• in constructive_ereal.v:

  • generalized from realDomainType to numDomainType
    • lemmas EFin_min and EFin_max
    • lemmas maxye, maxeNy, mineNy, minye

• in normedtype.v:

  • lemmas not_near_at_rightP, not_near_at_leftP
  • cvg_at_right_filter, cvg_at_left_filter
  • lemma open_subball
  • lemma interval_unbounded_setT

• in sequences.v,

  • generalized indexing from zero-based ones (0 <= k < n and k <oo) to m <= k < n and m <= k <oo
    • lemmas nondecreasing_series, ereal_nondecreasing_series, eseries_mkcondl, eseries_mkcondr, eq_eseriesl, nneseries_lim_ge, adde_def_nneseries, nneseriesD, nneseries_sum_nat, nneseries_sum,
  • lemmas nneseries_ge0, is_cvg_nneseries_cond, is_cvg_npeseries_cond, is_cvg_nneseries, is_cvg_npeseries, nneseries_ge0, npeseries_le0, lee_nneseries

• in derive.v:

  • lemmas decr_derive1_le0, incr_derive1_ge0

• in lebesgue_measure.v:

  • definition vitali_cover, lemma vitali_coverS

• in ftc.v:

  • lemmas increasing_cvg_at_right_comp, increasing_cvg_at_left_comp, decreasing_cvg_at_right_comp, decreasing_cvg_at_left_comp

Deprecated

• in Rstruct.v

  • lemma Rinvx

• file signed.v (use interval_inference.v instead)

• in interval_inference.v:

  • notation %:inum (use %:num instead)

• in lebesgue_measure.v:

  • lemmas measurable_fun_itv_co, measurable_fun_itv_oc

Removed

• in topology_structure.v, removed discrete_sing, discrete_nbhs, and discrete_space

• in nat_topology.v, removed discrete_nat

• in pseudometric_structure.v, removed discrete_ball_center, discrete_topology_type, and discrete_space_discrete.

• in signed.v/interval_inference.v

  • reserved notations [lb of _], [ub of _], [lbe of _] and [ube of _] (they were unused)
  • definitions wider_itv
  • Itv.subitv_map_itv (use num_spec_sub instead)
  • lemma le_map_itv_bound (use le_num_itv_bound instead)
  • lemmas opp_itv_le0_subproof, opp_itv_lt0_subproof

• in constructive_ereal.v:

  • lemmas num_abse_le, num_abse_lt
  • canonicals abse_snum, mule_snum, dadde_snum, dEFin_snum, adde_snum, oppe_snum, fine_snum, EFin_snum, ninfty_snum, pinfty_snum

• in sequences.v:

  • notations nneseries_pred0, eq_nneseries, nneseries0, ereal_cvgPpinfty, ereal_cvgPninfty (were deprecated since 0.6.0)
  • notations cvgPpinfty_lt, cvgPninfty_lt, cvgPpinfty_near, cvgPninfty_near, cvgPpinfty_lt_near, cvgPninfty_lt_near, ereal_cvgD_ninfty_ninfty, invr_cvg0, invr_cvg_pinfty, nat_dvg_real, nat_cvgPpinfty, ereal_squeeze, ereal_cvgD_pinfty_fin, ereal_cvgD_ninfty_fin, ereal_cvgD_pinfty_pinfty, ereal_cvgD, ereal_cvgB, ereal_is_cvgD, ereal_cvg_sub0, ereal_limD, ereal_cvgM_gt0_pinfty, ereal_cvgM_lt0_pinfty, ereal_cvgM_gt0_ninfty, ereal_cvgM_lt0_ninfty, ereal_cvgM, ereal_lim_sum, ereal_cvg_abs0, ereal_cvg_ge0, ereal_lim_ge, ereal_lim_le, dvg_ereal_cvg, ereal_cvg_real (were deprecated since 0.6.0)
  • lemmas __deprecated__cvgPpinfty_lt, __deprecated__cvgPninfty_lt, __deprecated__cvgPpinfty_near, __deprecated__cvgPninfty_near, __deprecated__cvgPpinfty_lt_near, __deprecated__cvgPninfty_lt_near, __deprecated__invr_cvg0, __deprecated__invr_cvg_pinfty, __deprecated__nat_dvg_real, __deprecated__nat_cvgPpinfty, __deprecated__ereal_squeeze, __deprecated__ereal_cvgD_pinfty_fin, __deprecated__ereal_cvgD_ninfty_fin, __deprecated__ereal_cvgD_pinfty_pinfty, __deprecated__ereal_cvgD, __deprecated__ereal_cvgB, __deprecated__ereal_is_cvgD, __deprecated__ereal_cvg_sub0, __deprecated__ereal_limD, __deprecated__ereal_cvgM_gt0_pinfty, __deprecated__ereal_cvgM_lt0_pinfty, __deprecated__ereal_cvgM_gt0_ninfty, __deprecated__ereal_cvgM_lt0_ninfty, __deprecated__ereal_cvgM, __deprecated__ereal_lim_sum, __deprecated__ereal_cvg_abs0, __deprecated__ereal_cvg_ge0, __deprecated__ereal_lim_ge, __deprecated__ereal_lim_le, __deprecated__dvg_ereal_cvg, __deprecated__ereal_cvg_real (were deprecated since 0.6.0)

• in normedtype.v

  • notations cvg_distP, cvg_distW, continuous_cvg_dist, cvg_dist2P, cvg_gt_ge, cvg_lt_le_, linear_bounded0 (deprecated since 0.6.0)
  • lemmas __deprecated__cvg_distW, __deprecated__continuous_cvg_dist, __deprecated__cvg_gt_ge, __deprecated__cvg_lt_le, __deprecated__linear_bounded0 (deprecated since 0.6.0)
  • notations cvg_distP, cvg_distW, continuous_cvg_dist, cvg_dist2P, cvg_gt_ge, cvg_lt_le_, linear_bounded0 (were deprecated since 0.6.0)
  • lemmas __deprecated__cvg_distW, __deprecated__continuous_cvg_dist, __deprecated__cvg_gt_ge, __deprecated__cvg_lt_le, __deprecated__linear_bounded0 (were deprecated since 0.6.0)

• in derive.v:

  • notations le0r_cvg_map, ler0_cvg_map, ler_cvg_map (deprecated since 0.6.0)
  • lemmas __deprecated__le0r_cvg_map, __deprecated__ler0_cvg_map, __deprecated__ler_cvg_map (deprecated since 0.6.0)

• in measure.v:

  • notation caratheodory_lim_lee (was deprecated since 0.6.0)

• in lebesgue_measure.v:

  • notations itv_cpinfty_pinfty, itv_opinfty_pinfty, itv_cninfty_pinfty, itv_oninfty_pinfty (were deprecated since 0.6.0)
  • lemmas __deprecated__itv_cpinfty_pinfty, __deprecated__itv_opinfty_pinfty, __deprecated__itv_cninfty_pinfty, __deprecated__itv_oninfty_pinfty (were deprecated since 0.6.0)

[1.8.0] - 2024-12-19

Added

• in mathcomp_extra.v:

  • lemma partition_disjoint_bigfcup

• in constructive_ereal.v:

  • notations \prod in scope ereal_scope
  • lemmas prode_ge0, prode_fin_num

• in num_topology.v:

  • lemma in_continuous_mksetP

• in normedtype.v:

  • lemmas continuous_within_itvcyP, continuous_within_itvNycP

• in realfun.v:

  • lemma cvg_nbhsP

• in measure.v:

  • lemma countable_bigcupT_measurable
  • definition discrete_measurable
  • lemmas discrete_measurable0, discrete_measurableC, discrete_measurableU

• in lebesgue_measure.v:

  • lemma measurable_indicP
  • lemma measurable_powRr

• in lebesgue_integral.v:

  • definition dyadic_approx (was Let A)
  • definition integer_approx (was Let B)
  • lemma measurable_sum
  • lemma integrable_indic
  • lemmas integrable_pushforward, integral_pushforward
  • lemma integral_measure_add

• in probability.v:

  • lemma expectation_def
  • notation 'M_
  • lemma integral_distribution (existing lemma integral_distribution has been renamed)

Changed

• in lebesgue_integrale.v
  • change implicits of measurable_funP

Renamed

• in classical_sets.v:

  • preimage_itv_o_infty -> preimage_itvoy
  • preimage_itv_c_infty -> preimage_itvcy
  • preimage_itv_infty_o -> preimage_itvNyo
  • preimage_itv_infty_c -> preimage_itvNyc

• in constructive_ereal.v:

  • maxeMr -> maxe_pMr
  • maxeMl -> maxe_pMl
  • mineMr -> mine_pMr
  • mineMl -> mine_pMl

• file homotopy_theory/path.v -> homotopy_theory/continuous_path.v

• in lebesgue_measure.v:

  • measurable_fun_indic -> measurable_indic
  • emeasurable_fun_sum -> emeasurable_sum
  • emeasurable_fun_fsum -> emeasurable_fsum
  • ge0_emeasurable_fun_sum -> ge0_emeasurable_sum

• in probability.v:

  • expectationM -> expectationZl
  • integral_distribution -> ge0_integral_distribution

Generalized

• in sequences.v:

  • lemmas cvg_restrict, cvg_centern, cvg_shiftn cvg_shiftS

• in lebesgue_integral.v:

  • lemma measurable_sfunP

• in probability.v:

  • definition random_variable
  • lemmas notin_range_measure, probability_range
  • definition distribution
  • lemma probability_distribution, integral_distribution
  • mixin MeasurableFun_isDiscrete
  • structure discreteMeasurableFun
  • definition discrete_random_variable
  • lemma dRV_dom_enum
  • definitions dRV_dom, dRV_enum, enum_prob
  • lemmas distribution_dRV, sum_enum_prob

Deprecated

• in lebesgue_integral.v:
  • lemma approximation

Removed

• in constructive_ereal.v

  • notation lee_opp (deprecated since 0.6.5)
  • notation lte_opp (deprecated since 0.6.5)

• in measure.v:

  • dynkin_setI_bigsetI (use big_ind instead)

• in lebesgue_measurable.v:

  • notation measurable_fun_power_pos (deprecated since 0.6.3)
  • notation measurable_power_pos (deprecated since 0.6.4)

• in lebesgue_integral.v:

  • lemma measurable_indic (was uselessly specializing measurable_fun_indic (now measurable_indic) from lebesgue_measure.v)
  • notation measurable_fun_indic (deprecation since 0.6.3)

[1.7.0] - 2024-11-22

Added

• package coq-mathcomp-reals depending on coq-mathcomp-classical with files

  • constructive_ereal.v
  • reals.v
  • real_interval.v
  • signed.v
  • itv.v
  • prodnormedzmodule.v
  • nsatz_realtype.v
  • all_reals.v

• package coq-mathcomp-experimental-reals depending on coq-mathcomp-reals with files

  • xfinmap.v
  • discrete.v
  • realseq.v
  • realsum.v
  • distr.v

• package coq-mathcomp-reals-stdlib depending on coq-mathcomp-reals with file

  • Rstruct.v

• package coq-mathcomp-analysis-stdlib depending on coq-mathcomp-analysis and coq-mathcomp-reals-stdlib with files

  • new file Rstruct_topology.v
  • showcase/uniform_bigO.v

• in file mathcomp_extra.v:

  • definition sigT_fun
  • definition idempotent_fun

• in boolp.v:

  • lemmas existT_inj1, surjective_existT
  • lemma existT_inj2
  • new lemmas uncurryK, and curryK

• new file topology_theory/one_point_compactification.v:

  • definitions one_point_compactification, and one_point_nbhs.
  • lemmas one_point_compactification_compact, one_point_compactification_some_nbhs, one_point_compactification_some_continuous, one_point_compactification_open_some, one_point_compactification_weak_topology, and one_point_compactification_hausdorff.

• new file topology_theory/sigT_topology.v:

  • definition sigT_nbhs.
  • lemmas sigT_nbhsE, existT_continuous, existT_open_map, existT_nbhs, sigT_openP, sigT_continuous, sigT_setUE, and sigT_compact.

• in file topology_theory/product_topology.v:

  • lemmas swap_continuous, prodA_continuous, and prodAr_continuous.

• in file topology_theory/order_topology.v:

  • lemmas min_continuous, min_fun_continuous, max_continuous, and max_fun_continuous.

• in file topology_theory/weak_topology.v:

  • lemma continuous_comp_weak

• in topology_theory/topology_structure.v:

  • definitions regopen, regclosed
  • lemmas closure_setC, interiorC, closureU, interiorU, closureEbigcap, interiorEbigcup, closure_open_regclosed, interior_closed_regopen, closure_interior_idem, interior_closure_idem
  • mixin isContinuous, type continuousType, structure Continuous
  • lemma continuousEP
  • definition mkcts

• in file topology_theory/subspace_topology.v:

  • lemmas continuous_subspace_setT, nbhs_prodX_subspace_inE, and continuous_subspace_prodP.
  • type continuousFunType, HB structure ContinuousFun

• in file topology_theory/subtype_topology.v:

  • lemmas subspace_subtypeP, subspace_sigL_continuousP, subspace_valL_continuousP', subspace_valL_continuousP, sigT_of_setXK, setX_of_sigTK, setX_of_sigT_continuous, and sigT_of_setX_continuous.

• in file separation_axioms.v:

  • lemmas compact_normal_local, and compact_normal.
  • lemma sigT_hausdorff.

• in file function_spaces.v:

  • definition eval
  • lemmas continuous_curry_fun, continuous_curry_cvg, eval_continuous, and compose_continuous

• new file tvs.v:

  • HB structures NbhsNmodule, NbhsZmodule, NbhsLmodule, TopologicalNmodule, TopologicalZmodule
  • notation topologicalLmoduleType, HB structure TopologicalLmodule
  • HB structures UniformZmodule, UniformLmodule
  • definition convex
  • mixin Uniform_isTvs
  • type tvsType, HB structure Tvs
  • HB factory TopologicalLmod_isTvs
  • lemma nbhs0N
  • lemma nbhsN
  • lemma nbhsT
  • lemma nbhsB
  • lemma nbhs0Z
  • lemma nbhZ

• in file normedtype.v:

  • definition type (in module completely_regular_uniformity)
  • lemmas normal_completely_regular, one_point_compactification_completely_reg, nbhs_one_point_compactification_weakE, locally_compact_completely_regular, and completely_regular_regular.
  • lemmas near_in_itvoy, near_in_itvNyo

• in measure.v:

  • lemma countable_measurable

• in realfun.v:

  • lemma cvgr_dnbhsP
  • definitions prodA, and prodAr
  • lemmas prodAK, prodArK, and swapK

• new file homotopy_theory/path.v:

  • definitions reparameterize, mk_path, and chain_path.
  • lemmas path_eqP, and chain_path_cts_point.

• new file homotopy_theory/wedge_sigT.v:

  • definitions wedge_rel, wedge, wedge_lift, pwedge.
  • lemmas wedge_lift_continuous, wedge_lift_nbhs, wedge_liftE, wedge_openP, wedge_pointE, wedge_point_nbhs, wedge_nbhs_specP, wedgeTE, wedge_compact, wedge_connected.
  • definitions wedge_fun, and wedge_prod.
  • lemmas wedge_fun_continuous, wedge_lift_funE, wedge_fun_comp, wedge_prod_pointE, wedge_prod_inj, wedge_prod_continuous, wedge_prod_open, wedge_hausdorff, and wedge_fun_joint_continuous.
  • definition bpwedge_shared_pt.
  • notations bpwedge, and bpwedge_lift.

• new file homotopy_theory/homotopy.v

Changed

• moved from Rstruct.v to Rstruct_topology.v

  • lemmas continuity_pt_nbhs, continuity_pt_cvg, continuity_ptE, continuity_pt_cvg', continuity_pt_dnbhs and nbhs_pt_comp

• moved from real_interval.v to normedtype.v

  • lemmas set_itvK, RhullT, RhullK, set_itv_setT, Rhull_smallest, le_Rhull, neitv_Rhull, Rhull_involutive, disj_itv_Rhull

• in topology.v:

  • lemmas subspace_pm_ball_center, subspace_pm_ball_sym, subspace_pm_ball_triangle, subspace_pm_entourage turned into local Let's

• in file normedtype.v:

  • changed completely_regular_space to depend on uniform separators which removes the dependency on R. The old formulation can be recovered easily with uniform_separatorP.
  • HB structure normedModule now depends on a Tvs instead of a Lmodule
  • Factory PseudoMetricNormedZmod_Lmodule_isNormedModule becomes PseudoMetricNormedZmod_Tvs_isNormedModule
  • Section prod_NormedModule now depends on a numFieldType

• in lebesgue_integral.v:

  • structure SimpleFun now inside a module HBSimple
  • structure NonNegSimpleFun now inside a module HBNNSimple
  • lemma cst_nnfun_subproof has now a different statement
  • lemma indic_nnfun_subproof has now a different statement

Renamed

• in normedtype.v:
  • near_in_itv -> near_in_itvoo
  • Section regular_topology to standard_topology

Generalized

• in lebesgue_integral.v:
  • generalized from sigmaRingType/realType to sigmaRingType/sigmaRingType
    • mixin isMeasurableFun
    • structure MeasurableFun
    • definition mfun
    • lemmas mfun_rect, mfun_valP, mfuneqP

Deprecated

• in topology_theory/topology_structure.v:
  • lemma closureC

Removed

• in cardinality.v:

  • lemma cst_fimfun_subproof

• in lebesgue_integral.v:

  • definition cst_mfun
  • lemma mfun_cst
  • lemma cst_mfun_subproof (use lemma measurable_cst instead)
  • lemma cst_nnfun_subproof (turned into a Let)
  • lemma indic_mfun_subproof (use lemma measurable_fun_indic instead)

[1.6.0] - 2024-10-25

Added

• new directory theories/topology with new files:

  • topology.v
  • bool_topology.v
  • compact.v
  • connected.v
  • matrix_topology.v
  • nat_topology.v
  • order_topology.v
  • product_topology.v
  • pseudometric_structure.v
  • subspace_topology.v
  • supremum_topology.v
  • topology_structure.v
  • uniform_structure.v
  • weak_topology.v
  • num_topology.v
  • quotient_topology.v

• in exp.v:

  • lemmas cvgr_expR, cvgn_expR

• in trigo.v:

  • lemmas derive1_atan, lt_atan, le_atan, cvgy_atan

• in lebesgue_measure.v:

  • lemmas RintegralZl, RintegralZr, Rintegral_ge0

Changed

• The file topology.v has been split into several files in the directory topology_theory. Unless stated otherwise, definitions, lemmas, etc. have been moved without changes. The same import will work as before, Require Import topology.v.

• in matrix_topology.v (new file):

  • lemmas mx_ball_center, mx_ball_sym, mx_ball_triangle, mx_entourage are now Local

• in weak_topology.v (new file):

  • lemmas wopT, wopI, wop_bigU are now Local

• in supremum_topology.v (new file):

  • lemmas sup_ent_filter, sup_ent_refl, sup_ent_inv, sup_ent_split, sup_ent_nbhs are now Local

• The function map_pair was moved from topology.v to mathcomp_extra.v.

• in forms.v:

  • notation 'e_

• in lebesgue_integral.v:

  • notation \x

Renamed

• in lebesgue_measure.v:
  • EFin_measurable_fun -> measurable_EFinP

Generalized

• in num_topology.v (new file):
  • lemma nbhs0_lt generalized from realType to realFieldType

Deprecated

• in pseudometric_structure.v (new file):
  • definition cvg_toi_locally (use cvgi_ballP instead)

Removed

• file topology.v (contents now in directory topology)

[1.5.0] - 2024-10-09

Added

• in mathcomp_extra.v:

  • lemma bij_forall

• in classical_sets.v:

  • lemma not_setD1

• in file classical_orders.v (new file),

  • definitions big_lexi_order, same_prefix, first_diff, big_lexi_le, and start_with.
  • lemmas same_prefix0, same_prefix_sym, same_prefix_leq, same_prefix_refl, same_prefix_trans, first_diff_sym, first_diff_unique, first_diff_SomeP, first_diff_NoneP, first_diff_lt, first_diff_eq, first_diff_dfwith, big_lexi_le_reflexive, big_lexi_le_anti, big_lexi_le_trans, big_lexi_le_total, start_with_prefix, leEbig_lexi_order, big_lexi_order_prefix_lt, big_lexi_order_prefix_gt, big_lexi_order_between, and big_lexi_order_interval_prefix.

• in filter.v (new file):

  • lemma in_nearW

• in topology.v:

  • lemma open_in_nearW

• new file separation_axioms.v

• in normedtype.v:

  • lemma cvgyNP
  • lemma limf_esup_ge0
  • lemma nbhs_left_ltBl
  • lemma within_continuous_continuous

• in sequences.v:

  • lemma nneseries_split_cond
  • lemma subset_lee_nneseries

• in exp.v:

  • lemma expR_gt1Dx

• in derive.v:

  • lemma exprn_derivable

• in realfun.v:

  • lemmas cvg_pinftyP, cvg_ninftyP

• in measure.v:

  • lemma measurable_fun_set1
  • lemma measurable_fun_set0

• in lebesgue_measure.v:

  • lemma vitali_coverS
  • lemma vitali_theorem_corollary
  • lemmas measurable_fun_itv_co, measurable_fun_itv_oc, measurable_fun_itv_cc

• in lebesgue_integral.v:

  • lemma integral_itv_bndoo

• in ftc.v:

  • lemmas increasing_image_oo, decreasing_image_oo, increasing_cvg_at_right_comp, increasing_cvg_at_left_comp, decreasing_cvg_at_right_comp, decreasing_cvg_at_left_comp,
  • lemma eq_integral_itv_bounded.
  • lemmas integration_by_substitution_decreasing, integration_by_substitution_oppr, integration_by_substitution_increasing

Changed

• theories/topology.v split into classical/filter.v and theories/topology.v

• moved from topology.v to filter.v

  • definition set_system, coercion set_system_to_set
  • mixin isFiltered, structures Filtered, PointedFiltered (with resp. types filteredType and pfilteredType)
  • mixin selfFiltered
  • factory hasNbhs
  • structures Nbhs, PointedNbhs (with resp. types nbhsType, pnbhsType)
  • definitions filter_from, filter_prod
  • definitions prop_near1, prop_near2
  • notations {near _, _}, \forall _ \near _, _, near _, _, {near _ & _, _}, \forall _ \near _ & _, _, \forall _ & _ \near _, _, \near _ & _, _
  • lemmas nearE, eq_near, nbhs_filterE
  • module NbhsFilter (with definition nbhs_simpl)
  • definition cvg_to, notation _ `=>` _
  • lemmas cvg_refl, cvg_trans, notation _ --> _
  • definitions type_of_filter, lim_in, lim
  • notations [lim _ in _], [cvg _ in _], cvg
  • definition eventually, notation \oo
  • lemmas cvg_prod, cvg_in_ex, cvg_ex, cvg_inP, cvgP, cvg_in_toP, cvg_toP, dvg_inP, dvgP, cvg_inNpoint, cvgNpoint
  • lemmas nbhs_nearE, near_nbhs, near2_curry, near2_pair, filter_of_nearI
  • definition near2E
  • module NearNbhs (with (re)definition near_simpl and ltac near_simpl)
  • lemma near_swap
  • classes Filter
  • lemmas filter_setT, filterP_strong
  • structure filter_on
  • definition filter_class
  • coercion filter_filter'
  • structure pfilter_on
  • definition pfilter_class
  • canonical pfilter_filter_on
  • coercion pfilter_filter_on
  • definiton PFilterType
  • instances filter_on_Filter, pfilter_on_ProperFilter
  • lemma nbhs_filter_onE, near_filter_onE
  • definition and canonical trivial_filter_on
  • lemmas filter_nbhsT, nearT, filter_not_empty_ex
  • lemma filter_ex_subproof, definition filter_ex
  • lemma filter_getP
  • record in_filter
  • module type in_filter, module PropInFilter, notation prop_of, definition prop_ofE, notation _ \is_near _, definition is_nearE
  • lemma prop_ofP
  • definition in_filterT
  • canonical in_filterI
  • lemma filter_near_of
  • fact near_key
  • lemmas mark_near, near_acc, near_skip_subproof
  • tactic notations near=>, near:, near do _
  • ltacs just_discharge_near, near_skip, under_near, end_near, done
  • lemmas have_near, near, nearW, filterE, filter_app, filter_app2, filter_app3, filterS2, filterS3, filter_const, in_filter_from, near_andP, nearP_dep, filter2P, filter_ex2, filter_fromP, filter_fromTP, filter_from_filter, filter_fromT_filter, filter_from_proper, filter_bigI, filter_forall, filter_imply
  • definition fmap
  • lemma fmapE
  • notations _ @[_ --> _], _ @[_ \oo], _ @ _, limn, cvgn
  • instances fmap_filter, fmap_proper_filter
  • definition fmapi, notations _ @[_ --> ], @ _
  • lemma fmapiE
  • instances fmapi_filter. fmapi_proper_filter
  • lemmas cvg_id, fmap_comp, appfilter, cvg_app, cvgi_app, cvg_comp, cvgi_comp, near_eq_cvg, eq_cvg, eq_is_cvg_in, eq_is_cvg, neari_eq_loc, cvg_near_const
  • definition continuous_at, notation continuous
  • lemma near_fun
  • definition globally, lemma globally0, instances globally_filter, globally_properfilter
  • definition frechet_filter, instances frechet_properfilter, frechet_properfilter_nat
  • definition at_point, instance at_point_filter
  • instances filter_prod_filter, filter_prod_proper, canonical prod_filter_on
  • lemmas filter_prod1, filter_prod2
  • definition in_filter_prod
  • lemmas near_pair, cvg_cst, cvg_snd, near_map, near_map2, near_mapi, filter_pair_set, filter_pair_near_of
  • module export NearMap
  • lemmas filterN, cvg_pair, cvg_comp2
  • definition cvg_to_comp_2
  • definition within, lemmas near_withinE, withinT, near_withinT, cvg_within, withinET, instance within_filter, canonical within_filter_on, lemma filter_bigI_within
  • definition subset_filter, instance subset_filter_filter, lemma subset_filter_proper
  • definition powerset_filter_from, instance powerset_filter_from_filter
  • lemmas near_small_set, small_set_sub, near_powerset_filter_fromP, powerset_filter_fromP, near_powerset_map, near_powerset_map_monoE
  • definitions principal_filter, principal_filter_type
  • lemmas principal_filterP, principal_filter_proper
  • class UltraFilter, lemma ultraFilterLemma
  • lemmas filter_image, proper_image, principal_filter_ultra, in_ultra_setVsetC, ultra_image
  • instance smallest_filter_filter
  • fixpoint filterI_iter
  • lemmas filterI_iter_sub, filterI_iterE
  • definition finI_from
  • lemmas finI_from_cover, finI_from1, finI_from_countable, finI_fromI, filterI_iter_finI, filterI_iter_finI
  • definition finI
  • lemmas finI_filter, filter_finI, meets_globallyl, meets_globallyr, meetsxx, proper_meetsxx
  • instance eventually_filter, canonicals eventually_filterType, eventually_pfilterType

• changed when moved from topology.v to filter.v

  • Build_ProperFilter -> Build_ProperFilter_ex
  • ProperFilter' -> ProperFilter
  • remove notation ProperFilter

• moved from topology.v to mathcomp_extra.v:

  • lemma and_prop_in
  • lemmas mem_inc_segment, mem_inc_segment

• moved from topology.v to boolp.v:

  • lemmas bigmax_geP, bigmax_gtP, bigmin_leP, bigmin_ltP

• moved from topology.v to separation_axioms.v: set_nbhs, set_nbhsP, accessible_space, kolmogorov_space, hausdorff_space, compact_closed, discrete_hausdorff, compact_cluster_set1, compact_precompact, open_hausdorff, hausdorff_accessible, accessible_closed_set1, accessible_kolmogorov, accessible_finite_set_closed, subspace_hausdorff, order_hausdorff, ball_hausdorff, Rhausdorff, close, closeEnbhs, closeEonbhs, close_sym, cvg_close, close_refl, cvgx_close, cvgi_close, cvg_toi_locally_close, closeE, close_eq, cvg_unique, cvg_eq, cvgi_unique, close_cvg, lim_id, lim_near_cst, lim_cst, entourage_close, close_trans, close_cvgxx, cvg_closeP, ball_close, normal_space, regular_space, compact_regular, uniform_regular, totally_disconnected, zero_dimensional, discrete_zero_dimension, zero_dimension_totally_disconnected, zero_dimensional_ray, type, countable_uniform_bounded, countable_uniform, sup_pseudometric, countable_uniformityT, gauge, iter_split_ent, gauge_ent, gauge_filter, gauge_refl, gauge_inv, gauge_split, gauge_countable_uniformity, uniform_pseudometric_sup, perfect_set, perfectTP, and perfectTP_ex.

• in numfun.v:

  • lemma gt0_funeposM renamed to ge0_funeposM and hypothesis weakened from strict to large inequality
  • lemma gt0_funenegM renamed to ge0_funenegM and hypothesis weakened from strict to large inequality
  • lemma lt0_funeposM renamed to le0_funeposM and hypothesis weakened from strict to large inequality
  • lemma lt0_funenegM renamed to le0_funenegM and hypothesis weakened from strict to large inequality

Renamed

• in file topology.v -> separation_axioms.v
  • totally_disconnected_cvg -> zero_dimensional_cvg.
  • perfect_set2 -> perfectTP_ex

Generalized

• in constructive_ereal.v:

  • lemmas maxeMr, maxeMl, mineMr, mineMr: hypothesis weakened from strict inequality to large inequality

• in sequences.v:

  • lemma eseries_mkcond
  • lemma nneseries_tail_cvg

• in exp.v:

  • lemmas expR_ge1Dx and expeR_ge1Dx (remove hypothesis)
  • lemma le_ln1Dx (weaken hypothesis)

• in derive.v:

  • lemma derivableX

• in lebesgue_integral.v:

  • lemma integral_setD1_EFin
  • lemmas integral_itv_bndo_bndc, integral_itv_obnd_cbnd
  • lemmas Rintegral_itv_bndo_bndc, Rintegral_itv_obnd_cbnd

Deprecated

• in separation_axioms.v:

  • definition cvg_toi_locally_close

• in realfun.v:

  • lemma lime_sup_ge0

Removed

• in constructive_ereal.v:

  • notation lte_spaddr (deprecated since 0.6)
  • notation gte_opp (deprecated since 0.6.0)
  • lemmas daddooe, daddeoo
  • notations desum_ninftyP, desum_ninfty, desum_pinftyP, desum_pinfty (deprecated since 0.6.0)
  • notation eq_pinftyP (deprecated since 0.6.0)

• in topology.v:

  • notation [filteredType _ of _]
  • definition fmap_proper_filter'
  • definition filter_map_proper_filter'
  • definition filter_prod_proper'

• in normedtype.v:

  • notation normmZ (deprecated since 0.6.0)
  • notation nbhs_image_ERFin (deprecated since 0.6.0)
  • notations ereal_limrM, ereal_limMr, ereal_limN (deprecated since 0.6.0)
  • notation norm_cvgi_map_lim (deprecated since 0.6.0)
  • notations ereal_cvgN, ereal_is_cvgN, ereal_cvgrM, ereal_is_cvgrM, ereal_cvgMr, ereal_is_cvgMr, ereal_cvgM (deprecated since 0.6.0)
  • notation cvg_dist, lemma __deprecated__cvg_dist (deprecated since 0.6.0)
  • notation cvg_dist2, lemma __deprecated__cvg_dist2 (deprecated since 0.6.0)
  • notation cvg_dist0, lemma __deprecated__cvg_dist0 (deprecated since 0.6.0)
  • notation ler0_addgt0P, lemma __deprecated__ler0_addgt0P (deprecated since 0.6.0)
  • notation cvg_bounded_real, lemma __deprecated__cvg_bounded_real (deprecated since 0.6.0)
  • notation linear_continuous0, lemma __deprecated__linear_continuous0 (deprecated since 0.6.0)

• in sequences.v:

  • notation nneseries_mkcond (was deprecated since 0.6.0)
  • notation squeeze, lemma __deprecated__squeeze (deprecated since 0.6.0)
  • notation cvgPpinfty, lemma __deprecated__cvgPpinfty (deprecated since 0.6.0)
  • notation cvgNpinfty, lemma __deprecated__cvgNpinfty (deprecated since 0.6.0)
  • notation cvgNninfty, lemma __deprecated__cvgNninfty (deprecated since 0.6.0)
  • notation cvgPninfty, lemma __deprecated__cvgPninfty (deprecated since 0.6.0)
  • notation ger_cvg_pinfty, lemma __deprecated__ger_cvg_pinfty (deprecated since 0.6.0)
  • notation ler_cvg_ninfty, lemma __deprecated__ler_cvg_ninfty (deprecated since 0.6.0)
  • notation lim_ge, lemma __deprecated__lim_ge (deprecated since 0.6.0)
  • notation lim_le, lemma __deprecated__lim_le (deprecated since 0.6.0)

[1.4.0] - 2024-09-24

Added

• in mathcomp_extra.v:

  • lemmas invf_ple, invf_lep

• in classical_sets.v:

  • scope relation_scope with delimiter relation
  • notation ^-1 in relation_scope (used to be a local notation)
  • lemma set_prod_invK (was a local lemma in normedtype.v)
  • definition diagonal, lemma diagonalP

• in functions.v:

  • lemmas mul_funC

• in set_interval.v:

  • lemma subset_itvSoo
  • definitions itv_is_ray, itv_is_bd_open, and itv_open_ends
  • lemmas itv_open_ends_rside, itv_open_ends_rinfty, itv_open_ends_lside, itv_open_ends_linfty, is_open_itv_itv_is_bd_openP, itv_open_endsI, itv_setU, itv_setI

• in topology.v:

  • lemma filterN
  • Structures PointedFiltered, PointedNbhs, PointedUniform, PseudoPointedMetric
  • definition order_topology
  • lemmas discrete_nat, rray_open, lray_open, itv_open, itv_open_ends_open, rray_closed, lray_closed, itv_closed, itv_closure, itv_closed_infimums, itv_closed_supremums, order_hausdorff, clopen_bigcup_clopen, zero_dimensional_ray, order_nbhs_itv, open_order_weak, real_order_nbhsE

• in normedtype.v:

  • lemmas not_near_inftyP, not_near_ninftyP
  • lemma ninftyN
  • lemma le_closed_ball
  • lemmas nbhs_right_ltW, cvg_patch

• in derive.v:

  • lemma derive_id
  • lemmas exp_derive, exp_derive1
  • lemma derive_cst
  • lemma deriveMr, deriveMl

• in sequences.v:

  • lemma cvg_geometric_eseries_half
  • theorem Baire
  • definition bounded_fun_norm
  • lemma bounded_landau
  • definition pointwise_bounded
  • definition uniform_bounded
  • theorem Banach_Steinhauss

• in numfun.v:

  • lemma indicI

• in measure.v:

  • lemma measurable_neg, measurable_or

• in lebesgue_measure.v:

  • definitions is_open_itv, open_itv_cover
  • lemmas outer_measure_open_itv_cover, outer_measure_open_le, outer_measure_open, outer_measure_Gdelta, negligible_outer_measure
  • lemmas measurable_fun_eqr, measurable_fun_indic, measurable_fun_dirac, measurable_fun_addn, measurable_fun_maxn, measurable_fun_subn, measurable_fun_ltn, measurable_fun_leq, measurable_fun_eqn
  • module NGenCInfty
    • definition G
    • lemmas measurable_itv_bounded, measurableE

• in lebesgue_integral.v:

  • lemma integralZr
  • lemma locally_integrableS
  • lemma integrable_locally_restrict
  • lemma near_davg
  • lemma lebesgue_pt_restrict

• in ftc.v:

  • lemmas integration_by_parts, Rintegration_by_parts
  • corollary continuous_FTC1_closed

Changed

• in topology.v:

  • removed the pointed assumptions from FilteredType, Nbhs, TopologicalType, UniformType, and PseudoMetricType.
  • if you want the original pointed behavior, use the p variants of the types, so ptopologicalType instead of topologicalType.
  • generalized most lemmas to no longer depend on pointedness. The main exception is for references to cvg and lim that depend on get for their definition.
  • pointed_principal_filter becomes principle_filter_type and requires only choiceType instead of pointedType
  • pointed_discrete_topology becomes discrete_topology_type and requires only choiceType instead of pointedType
  • renamed lemma discrete_pointedto discrete_space_discrete

• in function_space.v:

  • generalized most lemmas to no longer depend on pointedness.

• in normedtype.v:

  • remove superflous parameters in lemmas not_near_at_rightP and not_near_at_leftP
  • lemma continuous_within_itvP: change the statement to use the notation [/\ _, _ & _]

• moved from numfun.v to cardinality.v:

  • lemma fset_set_comp

• moved summability.v from theories to theories/showcase

• in lebesgue_measure.v:

  • remove redundant hypothesis from lemma pointwise_almost_uniform

• moved from lebesgue_measure.v to set_interval.v: is_open_itv, and open_itv_cover

• in lebesgue_integral.v:

  • lemma nice_lebesgue_differentiation: change the local integrability hypothesis to easy application

• in ftc.v:

  • lemma FTC1_lebesgue_pt, corollaries FTC1, FTC1Ny: integrability hypothesis weakened

Renamed

• in set_interval.v:

  • subset_itvS -> subset_itvScc

• in topology.v:

  • in mixin Nbhs_isUniform_mixin:
    • entourage_refl_subproof -> entourage_diagonal_subproof
  • in factory Nbhs_isUniform:
    • entourage_refl -> entourage_diagonal
  • in factory isUniform:
    • entourage_refl -> entourage_diagonal

• in lebesgue_measure.v:

  • measurable_exprn -> exprn_measurable
  • measurable_mulrl -> mulrl_measurable
  • measurable_mulrr -> mulrr_measurable
  • measurable_fun_pow -> measurable_funX
  • measurable_oppe -> oppe_measurable
  • measurable_abse -> abse_measurable
  • measurable_EFin -> EFin_measurable
  • measurable_oppr -> oppr_measurable
  • measurable_normr -> normr_measurable
  • measurable_fine -> fine_measurable
  • measurable_natmul -> natmul_measurable

• in lebesgue_integral.v

  • lemma integrable_locally -> open_integrable_locally

Generalized

• in derive.v:

  • lemma derivable_cst

• in lebesgue_measure.v:

  • lemma measurable_funX (was measurable_fun_pow)

• in lebesgue_integral.v

  • lemma ge0_integral_closed_ball

• in ftc.v:

  • lemma continuous_FTC2 (continuity hypothesis weakened)

Removed

• in lebesgue_measure.v:
  • notation measurable_fun_sqr (was deprecated since 0.6.3)
  • notation measurable_fun_exprn (was deprecated since 0.6.3)
  • notation measurable_funrM (was deprecated since 0.6.3)
  • notation emeasurable_fun_minus (was deprecated since 0.6.3)
  • notation measurable_fun_abse (was deprecated since 0.6.3)
  • notation measurable_fun_EFin (was deprecated since 0.6.3)
  • notation measurable_funN (was deprecated since 0.6.3)
  • notation measurable_fun_opp (was deprecated since 0.6.3)
  • notation measurable_fun_normr (was deprecated since 0.6.3)
  • notation measurable_fun_fine (was deprecated since 0.6.3)
• in topology.v:
  • turned into Let's (inside HB.builders):
    • lemmas nbhsE_subproof, openE_subproof
    • lemmas nbhs_pfilter_subproof, nbhsE_subproof, openE_subproof
    • lemmas open_fromT, open_fromI, open_from_bigU
    • lemmas finI_from_cover, finI_from_join
    • lemmas nbhs_filter, nbhs_singleton, nbhs_nbhs
    • lemmas ball_le, entourage_filter_subproof, ball_sym_subproof, ball_triangle_subproof, entourageE_subproof

[1.3.1] - 2024-08-09

Changed

• in wochoice.v:
  • two applications of the lemma in3W have been removed because they seem to cause a universe inconsistency when one loads the ring module of algebra-tactics

Generalized

• in reals.v:
  • lemma rat_in_itvoo (from realType to archiFieldType)

[1.3.0] - 2024-08-06

Added

• in mathcomp_extra.v:

  • lemma ge_floor
  • lemmas intr1D, intrD1, floor_eq, floorN
  • lemma invf_ltp

• new file wochoice.v:

  • definition prop_within
  • lemmas withinW, withinT, sub_within
  • notation {in <= _, _}
  • definitions maximal, minimal, upper_bound, lower_bound, preorder, partial_order, total_order, nonempty, minimum_of, maximum_of, well_order, chain, wo_chain
  • lemmas antisymmetric_wo_chain, antisymmetric_well_order, wo_chainW, wo_chain_reflexive, wo_chain_antisymmetric, Zorn's_lemma, Hausdorff_maximal_principle, well_ordering_principle

• in classical_sets.v:

  • lemma setCD
  • definition setY, notation `+`
  • lemmas setY0, set0Y, setYK, setYC, setYA, setIYl, mulrYr, setY_def, setYE, setYU, setYI, setYD, setYCT, setCYT, setYTC, setTYC
  • lemma setDU
  • lemmas setC_I, bigcup_subset
  • lemmas xsectionP, ysectionP

• in constructive_ereal.v:

  • lemmas lteD2rE, leeD2rE
  • lemmas lte_dD2rE, lee_dD2rE

• in reals.v:

  • lemma mem_rg1_floor

• in set_interval.v:

  • lemmas subset_itvl, subset_itvr, subset_itvS
  • lemma interval_set1

• in topology.v:

  • lemma ball_subspace_ball

• in ereal.v:

  • lemmas restrict_EFin

• in normedtype.v:

  • lemmas nbhs_lt, nbhs_le
  • lemma nbhs_right_ltDr

• in numfun.v:

  • lemma epatch_indic
  • lemma restrict_normr
  • lemmas funepos_le, funeneg_le

• in realfun.v:

  • lemma nondecreasing_at_left_is_cvgr
  • lemmas nondecreasing_at_left_at_right, nonincreasing_at_left_at_right

• in measure.v:

  • factory isAlgebraOfSets_setD
  • defintion setY_closed
  • factory isRingOfSets_setY
  • definition completed_measure_extension
  • lemma completed_measure_extension_sigma_finite
  • definition lim_sup_set
  • lemmas lim_sup_set_ub, lim_sup_set_cvg, lim_sup_set_cvg0

• in lebesgue_stieltjes_measure.v:

  • definition completed_lebesgue_stieltjes_measure

• in lebesgue_measure.v:

  • definition completed_lebesgue_measure
  • lemma completed_lebesgue_measure_is_complete
  • definition completed_algebra_gen
  • lemmas g_sigma_completed_algebra_genE, negligible_sub_caratheodory, completed_caratheodory_measurable

• in lebesgue_integral.v:

  • lemmas eq_Rintegral, Rintegral_mkcond, Rintegral_mkcondr, Rintegral_mkcondl, le_normr_integral, Rintegral_setU_EFin, Rintegral_set0, Rintegral_itv_bndo_bndc, Rintegral_itv_obnd_cbnd, Rintegral_set1, Rintegral_itvB
  • lemma integral_Sset1
  • lemma integralEpatch
  • lemma integrable_restrict
  • lemma le_integral
  • lemma null_set_integral
  • lemma EFin_normr_Rintegral

• in charge.v:

  • definition charge_variation
  • lemmas abse_charge_variation, charge_variation_continuous
  • definition induced
  • lemmas semi_sigma_additive_nng_induced, dominates_induced, integral_normr_continuous

• in ftc.v:

  • lemma FTC1 (specialization of the previous FTC1 lemma, now renamed to FTC1_lebesgue_pt)
  • lemma FTC1Ny
  • definition parameterized_integral
  • lemmas parameterized_integral_near_left, parameterized_integral_left, parameterized_integral_cvg_at_left, parameterized_integral_continuous
  • corollary continuous_FTC2

Changed

• in mathcomp_extra.v:

  • Notation "f ^-1" now at level 35 with f at next level

• in classical_sets.v:

  • lemmas Zorn and ZL_preorder now require a relation of type rel T instead of T -> T -> Prop

• moved from reals.v to mathcomp_extra.v

  • lemma lt_succ_floor: conclusion changed to match lt_succ_floor in MathComp, generalized to archiDomainType
  • generalized to archiDomainType: lemmas floor_ge0, floor_lt0, floor_natz, floor_ge_int, floor_neq0, floor_lt_int, ceil_ge, ceil_ge0, ceil_gt0, ceil_le0, ceil_ge_int, ceilN, abs_ceil_ge
  • generalized to archiDomainType and precondition generalized:
    • floor_le0
  • generalized to archiDomainType and renamed:
    • ceil_lt_int -> ceil_gt_int

• in reals.v:

  • definitions Rceil, Rfloor

• in topology.v:

  • lemmas subspace_pm_ball_center, subspace_pm_ball_sym, subspace_pm_ball_triangle, subspace_pm_entourage turned into local Let's

• in lebesgue_integral.v:

  • lemma measurable_int: argument mu now explicit

• moved from lebesgue_integral.v to ereal.v:

  • lemma funID

• moved from lebesgue_integral.v to numfun.v:

  • lemmas fimfunEord, fset_set_comp

• moved from lebesgue_integral.v to cardinality.v:

  • hint solve [apply: fimfunP]

Renamed

• in constructive_ereal.v:

  • lte_pdivr_mull -> lte_pdivrMl
  • lte_pdivr_mulr -> lte_pdivrMr
  • lte_pdivl_mull -> lte_pdivlMl
  • lte_pdivl_mulr -> lte_pdivlMr
  • lte_ndivl_mulr -> lte_ndivlMr
  • lte_ndivl_mull -> lte_ndivlMl
  • lte_ndivr_mull -> lte_ndivrMl
  • lte_ndivr_mulr -> lte_ndivrMr
  • lee_pdivr_mull -> lee_pdivrMl
  • lee_pdivr_mulr -> lee_pdivrMr
  • lee_pdivl_mull -> lee_pdivlMl
  • lee_pdivl_mulr -> lee_pdivlMr
  • lee_ndivl_mulr -> lee_ndivlMr
  • lee_ndivl_mull -> lee_ndivlMl
  • lee_ndivr_mull -> lee_ndivrMl
  • lee_ndivr_mulr -> lee_ndivrMr
  • eqe_pdivr_mull -> eqe_pdivrMl
  • lte_dadd -> lte_dD
  • lee_daddl -> lee_dDl
  • lee_daddr -> lee_dDr
  • gee_daddl -> gee_dDl
  • gee_daddr -> gee_dDr
  • lte_daddl -> lte_dDl
  • lte_daddr -> lte_dDr
  • gte_dsubl -> gte_dBl
  • gte_dsubr -> gte_dBr
  • gte_daddl -> gte_dDl
  • gte_daddr -> gte_dDr
  • lee_dadd2lE -> lee_dD2lE
  • lte_dadd2lE -> lte_dD2lE
  • lee_dadd2rE -> lee_dD2rE
  • lee_dadd2l -> lee_dD2l
  • lee_dadd2r -> lee_dD2r
  • lee_dadd -> lee_dD
  • lee_dsub -> lee_dB
  • lte_dsubl_addr -> lte_dBlDr
  • lte_dsubl_addl -> lte_dBlDl
  • lte_dsubr_addr -> lte_dBrDr
  • lte_dsubr_addl -> lte_dBrDl
  • gte_opp -> gteN
  • gte_dopp -> gte_dN
  • lte_le_add -> lte_leD
  • lee_lt_add -> lee_ltD
  • lte_le_dadd -> lte_le_dD
  • lee_lt_dadd -> lee_lt_dD
  • lte_le_sub -> lte_leB
  • lte_le_dsub -> lte_le_dB

• in classical_sets.v:

  • setM -> setX
  • in_setM -> in_setX
  • setMR -> setXR
  • setML -> setXL
  • setM0 -> setX0
  • set0M -> set0X
  • setMTT -> setXTT
  • setMT -> setXT
  • setTM -> setTX
  • setMI -> setXI
  • setM_bigcupr -> setX_bigcupr
  • setM_bigcupl -> setX_bigcupl
  • bigcup_setM_dep -> bigcup_setX_dep
  • bigcup_setM -> bigcup_setX
  • fst_setM -> fst_setX
  • snd_setM -> snd_setX
  • in_xsectionM -> in_xsectionX
  • in_ysectionM -> in_ysectionX
  • notin_xsectionM -> notin_xsectionX
  • notin_ysectionM -> notin_ysectionX
  • setSM -> setSX
  • bigcupM1l -> bigcupX1l
  • bigcupM1r -> bigcupX1r

• in cardinality.v:

  • countableMR -> countableXR
  • countableM -> countableX
  • countableML -> countableXL
  • infiniteMRl -> infiniteXRl
  • cardMR_eq_nat -> cardXR_eq_nat
  • finite_setM -> finite_setX
  • finite_setMR -> finite_setXR
  • finite_setML -> finite_setXL
  • fset_setM -> fset_setX

• in reals.v:

  • inf_lb -> inf_lbound
  • sup_ub -> sup_ubound
  • ereal_inf_lb -> ereal_inf_lbound
  • ereal_sup_ub -> ereal_sup_ubound

• in topology.v:

  • compact_setM -> compact_setX

• in measure.v:

  • measurable_restrict -> measurable_restrictT
  • setD_closed -> setSD_closed
  • measurableM -> measurableX

• in ftc.v:

  • FTC1 -> FTC1_lebesgue_pt

Generalized

• in constructive_ereal.v:

  • lemmas leeN2, lteN2 generalized from realDomainType to numDomainType

• in measure.v:

  • lemma measurable_restrict

Deprecated

• in constructive_ereal.v:

  • lemmas lte_opp2, lee_opp2 (use lteN2, leeN2 instead)

• in reals.v:

  • floor_le (use ge_floor instead)
  • le_floor (use Num.Theory.floor_le instead)
  • le_ceil (use ceil_ge instead)

• in lebesgue_integral.v:

  • lemmas integralEindic, integral_setI_indic

Removed

• in classical_sets.v:

  • inductive tower
  • lemma ZL'

• in reals.v:

  • definition floor (use Num.floor instead)
  • definition ceil (use Num.ceil instead)
  • lemmas floor0, floor1
  • lemma le_floor (use Num.Theory.floor_le instead)

• in topology.v, function_spaces.v, normedtype.v:

  • local notation to_set

[1.2.0] - 2024-06-06

Added

• in file mathcomp_extra.v:

  • module Order
    • definitions disp_t, default_display
  • lemma Pos_to_natE

• in classical_sets.v:

  • lemma bigcup_recl
  • notations \bigcup_(i >= n) F i and \bigcap_(i >= n) F i
  • lemmas bigcup_addn, bigcap_addn
  • lemmas setD_bigcup, nat_nonempty
  • hint nat_nonempty
  • lemma bigcup_bigsetU_bigcup
  • lemmas setDUD, setIDAC

• in Rstruct.v:

  • lemma IZRposE

• in signed.v:

  • lemma onem_nonneg_proof, definition onem_nonneg

• in esum.v:

  • lemma nneseries_sum_bigcup

• in normedtype.v:

  • lemma not_near_at_leftP

• in sequences.v:

  • lemma nneseries_recl
  • lemma nneseries_addn

• in realfun.v

  • lemmas total_variation_nondecreasing, total_variation_bounded_variation

• in measure.v:

  • definition subset_sigma_subadditive
  • factory isSubsetOuterMeasure
  • structure SigmaRing, notation sigmaRingType
  • factory isSigmaRing
  • lemma bigcap_measurable for sigmaRingType
  • lemma setDI_semi_setD_closed
  • lemmas powerset_lambda_system, lambda_system_smallest, sigmaRingType_lambda_system
  • definitions niseq_closed, sigma_ring (notation <<sr _ >>), monotone (notation <<M _ >>)
  • lemmas smallest_sigma_ring, sigma_ring_monotone, g_sigma_ring_monotone, sub_g_sigma_ring, setring_monotone_sigma_ring, g_monotone_monotone, g_monotone_setring, g_monotone_g_sigma_ring, monotone_setring_sub_g_sigma_ring
  • lemmas powerset_sigma_ring, g_sigma_ring_strace, setI_g_sigma_ring, subset_strace
  • lemma measurable_and
  • lemma measurableID
  • lemma strace_sigma_ring

• in lebesgue_measure.v:

  • lemma measurable_fun_ler
  • lemmas measurable_natmul, measurable_fun_pow

• in lebesgue_integral.v:

  • lemmas integrableMl, integrableMr

• in probability.v:

  • definition bernoulli_pmf
  • lemmas bernoulli_pmf_ge0, bernoulli_pmf1, measurable_bernoulli_pmf
  • definition bernoulli (equipped with the probability structure)
  • lemmas bernoulli_dirac, bernoulliE, integral_bernoulli, measurable_bernoulli, measurable_bernoulli2
  • definition binomial_pmf
  • lemmas binomial_pmf_ge0, measurable_binomial_pmf
  • definitions binomial_prob (equipped with the probability structure), bin_prob
  • lemmas bin_prob0, bin_prob1, binomial_msum, binomial_probE, integral_binomial, integral_binomial_prob, measurable_binomial_prob
  • definition uniform_pdf
  • lemmas measurable_uniform_pdf, integral_uniform_pdf, integral_uniform_pdf1
  • definition uniform_prob (equipped with the probability structure)
  • lemmas dominates_uniform_prob, integral_uniform

• new file theories/all_analysis.v

Changed

• in forms.v:

  • notation u ``_ _

• in sequences.v:

  • definition expR is now HB.locked
  • equality reversed in lemma eq_bigcup_seqD
  • eq_bigsetU_seqD renamed to nondecreasing_bigsetU_seqD and equality reversed

• in trigo.v:

  • definitions sin, cos, acos, asin, atan are now HB.locked

• in measure.v:

  • change the hypothesis of measurable_fun_bool
  • mixin AlgebraOfSets_isMeasurable renamed to hasMeasurableCountableUnion and made to inherit from SemiRingOfSets
  • rm hypo and variable in lemma smallest_monotone_classE and rename to smallest_lambda_system
  • rm hypo in lemma monotone_class_g_salgebra and renamed to g_salgebra_lambda_system
  • rm hypo in lemma monotone_class_subset and renamed to lambda_system_subset
  • notation <<m _, _>> changed to <<l _, _>>, notation <<m _>> changed to <<l _>>

• moved from lebesgue_measure.v to measure.v:

  • definition strace
  • lemma sigma_algebra_strace

Renamed

• in classical_sets.v:

  • notin_set -> notin_setE

• in constructive_ereal.v:

  • gee_pmull -> gee_pMl
  • gee_addl -> geeDl
  • gee_addr -> geeDr
  • gte_addl -> gteDl
  • gte_addr -> gteDr
  • lte_subl_addr -> lteBlDr
  • lte_subl_addl -> lteBlDl
  • lte_subr_addr -> lteBrDr
  • lte_subr_addl -> lteBrDl
  • lee_subl_addr -> leeBlDr
  • lee_subl_addl -> leeBlDl
  • lee_subr_addr -> leeBrDr
  • lee_subr_addl -> leeBrDl
  • num_lee_maxr -> num_lee_max
  • num_lee_maxl -> num_gee_max
  • num_lee_minr -> num_lee_min
  • num_lee_minl -> num_gee_min
  • num_lte_maxr -> num_lte_max
  • num_lte_maxl -> num_gte_max
  • num_lte_minr -> num_lte_min
  • num_lte_minl -> num_gte_min

• in signed.v:

  • num_le_maxr -> num_le_max
  • num_le_maxl -> num_ge_max
  • num_le_minr -> num_le_min
  • num_le_minl -> num_ge_min
  • num_lt_maxr -> num_lt_max
  • num_lt_maxl -> num_gt_max
  • num_lt_minr -> num_lt_min
  • num_lt_minl -> num_gt_min

• in measure.v:

  • sub_additive -> subadditive
  • sigma_sub_additive -> measurable_subset_sigma_subadditive
  • content_sub_additive -> content_subadditive
  • ring_sigma_sub_additive -> ring_sigma_subadditive
  • Content_SubSigmaAdditive_isMeasure -> Content_SigmaSubAdditive_isMeasure
  • measure_sigma_sub_additive -> measure_sigma_subadditive
  • measure_sigma_sub_additive_tail -> measure_sigma_subadditive_tail
  • bigcap_measurable -> bigcap_measurableType
  • monotone_class -> lambda_system
  • monotone_class_g_salgebra -> g_sigma_algebra_lambda_system
  • smallest_monotone_classE -> smallest_lambda_system
  • dynkin_monotone -> dynkin_lambda_system
  • dynkin_g_dynkin -> g_dynkin_dynkin
  • salgebraType -> g_sigma_algebraType
  • g_salgebra_measure_unique_trace -> g_sigma_algebra_measure_unique_trace
  • g_salgebra_measure_unique_cover -> g_sigma_algebra_measure_unique_cover
  • g_salgebra_measure_unique -> g_sigma_algebra_measure_unique
  • setI_closed_gdynkin_salgebra -> setI_closed_g_dynkin_g_sigma_algebra

• in lebesgue_integral.v:

  • integral_measure_add -> ge0_integral_measure_add
  • integral_pushforward -> ge0_integral_pushforward

Generalized

• in Rstruct.v:

  • lemmas RinvE, RdivE

• in constructive_ereal.v:

  • gee_pMl (was gee_pmull)

• in sequences.v:

  • lemmas eseries0, nneseries_split

• in measure.v:

  • lemmas outer_measure_subadditive, outer_measureU2 (from semiRingOfSetType to Type)
  • lemmas caratheodory_measurable_mu_ext, measurableM, measure_dominates_trans, ess_sup_ge0 definitions preimage_classes, measure_dominates, ess_sup (from measurableType to semiRingOfSetsType)
  • lemmas measurable_prod_measurableType, measurable_prod_g_measurableTypeR (from measurableType to algebraOfSetsType)
  • from measurableType to sigmaRingType
    • lemmas bigcup_measurable, bigcapT_measurable
    • definition measurable_fun
    • lemmas measurable_id, measurable_comp, eq_measurable_fun, measurable_cst, measurable_fun_bigcup, measurable_funU, measurable_funS, measurable_fun_if
    • lemmas semi_sigma_additiveE, sigma_additive_is_additive, measure_sigma_additive
    • definitions pushforward, dirac
    • lemmas diracE, dirac0, diracT, finite_card_sum, finite_card_dirac, infinite_card_dirac
    • definitions msum, measure_add, mscale, mseries, mrestr
    • lemmas msum_mzero, measure_addE
    • definition sfinite_measure
    • mixin isSFinite, structure SFiniteMeasure
    • structure FiniteMeasure
    • factory Measure_isSFinite
    • lemma negligible_bigcup
    • definition ae_eq
    • lemmas ae_eq0, ae_eq_comp, ae_eq_funeposneg, ae_eq_refl, ae_eq_sym, ae_eq_trans, ae_eq_sub, ae_eq_mul2r, ae_eq_mul2l, ae_eq_mul1l, ae_eq_abse, ae_eq_subset
  • from measurableType to sigmaRingType and from realType to realFieldType
    • definition mzero
  • from realType to realFieldType:
    • lemma sigma_finite_mzero

• in lebesgue_measure.v:

  • from measurableType to sigmaRingType
    • section measurable_fun_measurable

• in lebesgue_integral.v:

  • lemma ge0_integral_bigcup
  • lemma ge0_emeasurable_fun_sum
  • from measurableType to sigmaRingType
    • mixin isMeasurableFun
    • structure SimpleFun
    • structure NonNegSimpleFun
    • sections fimfun_bin, mfun_pred, sfun_pred, simple_bounded
    • lemmas nnfun_muleindic_ge0, mulemu_ge0, nnsfun_mulemu_ge0
    • section sintegral_lemmas
    • lemma eq_sintegral
    • section sintegralrM

• in probability.v:

  • lemma markov

Deprecated

• in classical_sets.v:
  • notin_set (use notin_setE instead)

Removed

• in forms.v

  • canonical rev_mulmx
  • structure revop

• in reals.v

  • lemma inf_lower_bound (use inf_lb instead)

• in derive.v:

  • definition mulr_rev
  • canonical rev_mulr
  • lemmas mulr_is_linear, mulr_rev_is_linear

• in measure.v:

  • lemmas prod_salgebra_set0, prod_salgebra_setC, prod_salgebra_bigcup (use measurable0, measurableC, measurable_bigcup instead)

• in lebesgue_measure.v:

  • lemmas stracexx, strace_measurable

• in lebesgue_integral.v:

  • integrablerM, integrableMr (were deprecated since version 0.6.4)

[1.1.0] - 2024-03-31

Added

• in mathcomp_extra.v

  • lemma invf_plt

• in contra.v:

  • in module Internals
    • variant equivT
    • definitions equivT_refl, equivT_transl, equivT_sym, equivT_trans, equivT_transr, equivT_Prop, equivT_LR (hint view), equivT_RL (hint view)
  • definition notP
  • hint view for move/ and apply/ for Internals.equivT_LR, Internals.equivT_RL

• in set_interval.v

  • lemmas setDitv1r, setDitv1l
  • lemmas set_itvxx, itv_bndbnd_setU

• in reals.v

  • lemma abs_ceil_ge

• in topology.v:

  • lemmas nbhs_infty_ger, nbhs0_ltW, nbhs0_lt

• file function_spaces.v

• in normedtype.v

  • lemma closed_ball_ball
  • lemma ball_open_nbhs
  • definition completely_regular_space
  • lemmas point_uniform_separator, and uniform_completely_regular.

• in exp.v

  • lemma ln_lt0
  • lemma expRM_natr

• in numfun.v

  • lemma cvg_indic

• in lebesgue_integral.v

  • lemma ge0_integralZr
  • lemma locally_integrable_indic
  • definition davg, lemmas davg0, davg_ge0, davgD, continuous_cvg_davg
  • definition lim_sup_davg, lemmas lim_sup_davg_ge0, lim_sup_davg_le, continuous_lim_sup_davg, lim_sup_davgB, lim_sup_davgT_HL_maximal
  • definition lebesgue_pt, lemma continuous_lebesgue_pt
  • lemma integral_setU_EFin
  • lemmas integral_set1, ge0_integral_closed_ball, integral_setD1_EFin, integral_itv_bndo_bndc, integral_itv_obnd_cbnd
  • lemma lebesgue_differentiation
  • lemma lebesgue_density
  • definition nicely_shrinking, lemmas nicely_shrinking_gt0, nicely_shrinking_lty, nice_lebesgue_differentiation

• new file ftc.v:

  • lemmas FTC1, continuous_FTC1

Changed

• moved from topology.v to function_spaces.v: prod_topology, product_topology_def, proj_continuous, dfwith_continuous, proj_open, hausdorff_product, tychonoff, perfect_prod, perfect_diagonal, zero_dimension_prod, totally_disconnected_prod, separate_points_from_closed, weak_sep_cvg, weak_sep_nbhsE, weak_sep_openE, join_product, join_product_continuous, join_product_open, join_product_inj, join_product_weak, fct_ent, fct_ent_filter, fct_ent_refl, fct_ent_inv, fct_ent_split, cvg_fct_entourageP, fun_complete, fct_ball, fct_ball_center, fct_ball_sym, fct_ball_triangle, fct_entourage, cvg_switch_1, cvg_switch_2, cvg_switch, uniform_fun, uniform_nbhs, uniform_entourage, restricted_cvgE, pointwise_cvgE, uniform_fun_family, uniform_set1, uniform_subset_nbhs, uniform_subset_cvg, pointwise_uniform_cvg, cvg_sigL, eq_in_close, hausdorrf_close_eq_in, uniform_restrict_cvg, uniform_nbhsT, cvg_uniformU, cvg_uniform_set0, fam_cvgP, family_cvg_subset, family_cvg_finite_covers, fam_cvgE, fam_nbhs, fam_compact_nbhs, compact_open, compact_openK, compact_openK_nbhs, compact_open_of_nbhs, compact_open_def, compact_open_cvgP, compact_open_open, compact_open_fam_compactP, compactly_in, compact_cvg_within_compact, uniform_limit_continuous, uniform_limit_continuous_subspace, singletons, pointwise_cvg_family_singleton, pointwise_cvg_compact_family, pointwise_cvgP, equicontinuous, equicontinuous_subset, equicontinuous_subset_id, equicontinuous_continuous_for, equicontinuous_continuous, pointwise_precompact, pointwise_precompact_subset, pointwise_precompact_precompact, uniform_pointwise_compact, precompact_pointwise_precompact, pointwise_cvg_entourage, equicontinuous_closure, small_ent_sub, pointwise_compact_cvg, pointwise_compact_closure, pointwise_precompact_equicontinuous, compact_equicontinuous, precompact_equicontinuous, Ascoli, continuous_curry, continuous_uncurry_regular, continuous_uncurry, curry_continuous, and uncurry_continuous.

• moved from cantor.v to topology.v:

  • lemma discrete_bool_compact
  • definition pointed_principal_filter
  • definition pointed_discrete_topology
  • lemma discrete_pointed

• in measure.v:

  • lemma sigma_finiteP generalized to an equivalence and changed to use [/\ ..., .. & ....]

• move from kernel.v to measure.v

  • definition mset, pset, pprobability
  • lemmas lt0_mset, gt1_mset

Renamed

• in constructive_ereal.v:

  • lee_addl -> leeDl
  • lee_addr -> leeDr
  • lee_add2l -> leeD2l
  • lee_add2r -> leeD2r
  • lee_add -> leeD
  • lee_sub -> leeB
  • lee_add2lE -> leeD2lE
  • lte_add2lE -> lteD2lE
  • lee_oppl -> leeNl
  • lee_oppr -> leeNr
  • lte_oppr -> lteNr
  • lte_oppl -> lteNl
  • lte_add -> lteD
  • lte_addl -> lteDl
  • lte_addr -> lteDr

• in exp.v:

  • expRMm -> expRM_natl

• in measure.v:

  • Measure_isSFinite_subdef -> isSFinite
  • sfinite_measure_subdef -> s_finite
  • SigmaFinite_isFinite -> isFinite
  • FiniteMeasure_isSubProbability -> isSubProbability

• in lebesgue_integral.v

  • integral_setU -> ge0_integral_setU
  • subset_integral -> ge0_subset_integral

Generalized

• in realfun.v
  • lemma lime_sup_le

Removed

• in topology.v:

  • definition pointwise_fun
  • module PtwsFun

• in mathcomp_extra.v:

  • notations eqLHS and eqRHS (they are eqbLHS and eqbRHS in mathcomp since 1.15.0)

[1.0.0] - 2024-01-26

Added

• in constructive_ereal.v:

  • definition dEFin
  • notations %:dE, %:E (ereal_dual_scope)
  • notation \bar^d ... (type_scope) for dual extended real numbers
  • instance using isNmodule.Build for \bar
  • instances using Choice.on and isNmodule.Build for \bar^d
  • lemma EFin_semi_additive
  • lemmas dEFinE, dEFin_semi_additive
  • instance using isSemiAdditive.Build for \bar^d
  • canonical dEFin_snum

• in reals.v:

  • definition Rint_pred

• in topology.v

  • definition set_system, identity coercion set_system_to_set with instances using Equality.on, Choice.on, Pointed.on, isFiltered.Build
  • mixin selfFiltered, factory hasNbhs, structure Nbhs, type nbhsType
  • instance for matrices using selfFiltered.Build
  • lemmas cvg_in_ex, cvg_inP, cvg_in_toP, dvg_inP, cvg_inNpoint, eq_is_cvg_in
  • notations E @[ x \oo ], limn, cvgn
  • definition continuous_at
  • definitions weak_topology, sup_topology, prod_topology
  • definition prod_topo_apply
  • definition discrete_topology
  • instead of zmodType using isPointed.Build
  • definition pointwise_cvgE, instance using Uniform.copy for {ptws _ -> _}
  • definition compact_open_of_nbhs, lemmas compact_openK_nbhsE_subproof, compact_openK_openE_subproof

• in cantor.v:

  • definition pointed_principal_filter, instances using Pointed.on and hasNbhs.Build
  • definition pointed_discrete_topology
  • lemma discrete_pointed
  • lemma discrete_bool_compact

• in normedtype.v:

  • definition urysohnType with instances using Pointed.on and isUniform.Build

• in derive.v:

  • lemma cvg_at_rightE, cvg_at_leftE

• in convex.v:

  • definition convex_lmodType with instances using Choice.on and isConvexSpace.Build
  • definition convex_realDomainType with instance using isConvexSpace.Build

• in lebesgue_stieltjes_measure.v:

  • instance on ocitv_type using Pointed.on

• in lebesgue_integral.v:

  • mixin isNonNegFun, notations {nnfun _ >-> _}, [nnfun of _]
  • section ring
    • lemmas fimfun_mulr_closed, instances using GRing.isMulClosed.Build, [SubZmodule_isSubRing of ... by <:]
    • lemmas fimfunM, fimfun1, fimfun_prod, fimfunX,
    • lemma indic_fimfun_subproof, instance using indic_fimfun_subproof
    • definition indic_fimfun
    • instance using FImFun.copy, definition scale_fimfun
  • section comring
    • instance using [SubRing_isSubComRing of ... by <:]
    • instance using FImFun.copy
  • lemmas fimfunE, fimfunEord, trivIset_preimage1, trivIset_preimage1_in
  • section fimfun_bin
    • lemma max_fimfun_subproof, instance using max_fimfun_subproof
  • factory FiniteDecomp

• in charge.v:

  • cscale instances using SigmaFinite_isFinite.Build and isAdditiveCharge.Build

Changed

• in boolp.v:

  • in lemma gen_choiceMixin: Choice.mixin_of -> hasChoice
  • in definition gen_eqMixin: EqMixin -> hasDecEq.Build
  • canonical dep_arrow_eqType -> instance using gen_eqMixin
  • canonical dep_arrow_choiceType -> instance using gen_choiceMixin
  • canonical Prop_eqType -> instance using gen_eqMixin
  • canonical Prop_choiceType -> instance using gen_choiceMixin
  • canonical classicType_eqType -> instance using gen_eqMixin
  • canonical classicType_choiceType -> instance using gen_choiceMixin
  • canonical eclassicType_eqType -> instance using Equality.copy
  • canonical eclassicType_choiceType -> instance using gen_choiceMixin
  • definition porderMixin and canonical porderType -> instance using isPOrder.Build
  • definition latticeMixin and canonical latticeType -> instance using POrder_isLattice.Build

• in classical_sets.v:

  • canonicals setU_monoid, setU_comoid, setU_mul_monoid, setI_monoid, setI_comoid, setI_mul_monoid, setU_add_monoid, setI_add_monoid -> instances using isComLaw.Build, isMulLaw.Build, isComLaw.Build, isMulLaw.Build, isAddLaw.Build, isAddLaw.Build
  • module Pointed (packed class) -> mixin isPointed, structure Pointed
  • canonical arrow_pointedType and definition dep_arrow_pointedType -> instance using isPointed.Build
  • canonicals unit_pointedType, bool_pointedType, Prop_pointedType, nat_pointedType, prod_pointedType, matrix_pointedType, option_pointedType, pointed_fset -> instances using isPointed.Build
  • module Empty (packed class) -> mixin isEmpty, structure Empty, factories Choice_isEmpty, Type_isEmpty
  • definition False_emptyMixin and canonicals False_eqType, False_choiceType, False_countType, False_finType, False_emptyType -> instance using Type_isEmpty.Build
  • definition void_emptyMixin and canonical void_emptyType -> instance using isEmpty.Build
  • definition orderMixin and canonicals porderType, latticeType, distrLatticeType -> instances using Choice.copy and isMeetJoinDistrLattice.Build
  • canonicals bLatticeType, tbLatticeType, bDistrLatticeType, tbDistrLatticeType -> instances using hasBottom.Build and hasTop.Build
  • canonical cbDistrLatticeType -> instance using hasRelativeComplement.Build
  • canonical ctbDistrLatticeType -> instance using hasComplement.Build

• in functions.v:

  • notation split
  • notation \_ moved from fun_scope to function_scope
  • notations pinv, pPbij, pPinj, injpPfun, funpPinj
  • in definition fct_zmodMixin: ZmodMixin -> isZmodule.Build
  • canonical fct_zmodType -> instance using fct_zmodMixin
  • in definition fct_ringMixin: RingMixin -> Zmodule_isRing.Build
  • canonical fct_ringType -> instance using fct_ringMixin
  • canonical fct_comRingType -> definition and instance using Ring_hasCommutativeMul.Build and fct_comRingType
  • definition fct_lmodMixin and canonical fct_lmodType -> definition fct_lmodMixin and instance using fct_lmodMixin

• in cardinality.v:

  • canonical rat_pointedType -> instance using isPointed.Build
  • canonical fimfun_subType -> instance using isSub.Build
  • definition fimfuneqMixin and canonical fimfuneqType -> instance using [Equality of ... by <:]
  • definition fimfunchoiceMixin and canonical fimfunchoiceType -> instance using [Choice of ... by <:]
  • canonicals fimfun_add, fimfun_zmod, fimfun_zmodType, and definition fimfun_zmodMixin -> instances using isZmodClosed.Build and [SubChoice_isSubZmodule of ... <:]

• in signed.v:

  • definitions signed_subType, signed_choiceMixin, signed_porderMixin, canonicals signed_eqMixin, signed_eqType, signed_choiceType, signed_porderType -> instances using [isSub for ...] and [POrder of ... by <:]
  • in lemma signed_le_total: totalPOrderMixin -> total
  • canonicals signed_latticeType, signed_distrLatticeType, signed_orderType -> instance using Order.POrder_isTotal.Build

• in constructive_ereal.v:

  • definition ereal_eqMixin and canonical ereal_eqType -> instance using hasDecEq.Build
  • definition ereal_choiceMixin and canonical ereal_choiceType -> instance using Choice.copy
  • definition ereal_countMixin and ereal_countType -> instance using PCanIsCountable
  • definition ereal_porderMixin and canonical Choice.copy -> instance using isPOrder.Build
  • in lemma le_total_ereal : le_total_ereal -> total
  • canonicals ereal_latticeType, ereal_distrLatticeType, ereal_orderType, ereal_blatticeType, ereal_tblatticeType, lemmas ereal_blatticeMixin, ereal_blatticeMixin -> instances using POrder_isTotal.Build, hasBottom.Build, hasTop.Build
  • canonicals adde_monoid, adde_comoid, mule_mulmonoid -> instance using isMulLaw.Build
  • notations maxe, mine: fun_scope -> function_scope
  • canonicals mule_monoid, mule_comoid -> instance using isComLaw.Build
  • canonicals maxe_monoid, maxe_comoid -> instance using isLaw.Build

• in reals.v:

  • module Real (packed class) -> mixin ArchimedeanField_isReal with fields sup_upper_bound_subdef, sup_adherent_subdef, structure Real
  • canonicals Rint_keyed, Rint_opprPred, Rint_addrPred, Rint_mulrPred, Rint_zmodPred, Rint_semiringPred, Rint_smulrPred, Rint_subringPred -> instance using GRing.isSubringClosed.Build

• in topology.v:

  • canonicals linear_eqType, linear_choiceType -> instances using gen_eqMixin, gen_choiceMixin
  • canonical gen_choiceMixin -> instance using isPointed.Build
  • module Filtered (packed class) -> mixin isFiltered with field nbhs, structure Filtered
  • now use set_system:
    • definitions filter_from, filter_prod, cvg_to, type_of_filter, lim_in, Build_ProperFilter, filter_ex, fmap, fmapi, globally, in_filter_prod, within, subset_filter, powerset_filter_from, principal_filter, locally_of, sup_subbase, cluster, compact, near_covering, near_covering_within, compact_near, nbhs_, weak_ent, sup_ent, cauchy, cvg_cauchy, cauchy_ex.Build, cauchy_ball
    • classes Filter, ProperFilter', UltraFilter
    • instances fmap_proper_filter, fmapi_filter, fmapi_proper_filter, filter_prod_filter, filter_prod1, filter_prod2
    • record in_filter
    • structure filter_on
    • variant nbhs_subspace_spec
    • lemmas nearE, eq_near, nbhs_filterE, cvg_refl, cvg_trans, near2_curry, near_swap, filterP_strong, filter_nbhsT, nearT, filter_not_empty_ex, filter_ex_subproof, filter_getP, near, nearW, filterE, filter_app, filter_app2, filter_app3, filterS2, filterS3, nearP_dep, filter2P, filter_ex2, filter_fromP, filter_fromTP, filter_bigIP, filter_forall, filter_imply, fmapEP, fmapiE, cvg_id, appfilterP, cvg_app, cvgi_app, cvg_comp, cvgi_comp, near_eq_cvg, eq_cvg, neari_eq_loc, cvg_near_const, near_pair, near_map, near_map2, near_mapi, filter_pair_set, filter_pair_near_of, cvg_pair, cvg_comp2, near_powerset_map, near_powerset_map_monoE, cvg_fmap, continuous_cvg, continuous_is_cvg, continuous2_cvg, cvg_near_cst, is_cvg_near_cst, cvg_cst, is_cvg_cst, fmap_within_eq, cvg_image, cvg_fmap2, cvg_within_filter, cvg_app_within, meets_openr, meets_openl, meetsxx, proper_meetsxx, ultra_cvg_clusterE, ultraFilterLemma, compact_ultra, proper_image, in_ultra_setVsetC, ultra_image, filter_finI, close_cvg, discrete_cvg, nbhs_E, cvg_closeP, cvg_mx_entourageP, cvg_fct_entourageP, fcvg_ball2P, cvg_ball2P, cauchy_cvgP, mx_complete, Uniform_isComplete.Build, cauchy_ballP, cauchy_exP, cauchyP, compact_cauchy_cvg, pointwise_cvgE, pointwise_uniform_cvg, cvg_sigL, uniform_restrict_cvg, cvg_uniformU, cvg_uniform_set0, fam_cvgP, family_cvg_subset, family_cvg_finite_covers, fam_cvgE, Nbhs_isTopological, compact_open_fam_compactP, compact_cvg_within_compact, nbhs_subspace, subspace_cvgP, uniform_limit_continuous, uniform_limit_continuous_subspace, pointwise_compact_cvg
    • t in module type PropInFilterSig
  • canonical matrix_filtered -> instance using isFiltered.Build
  • now use nbhs instead of [filter of ...]
    • notations -->, E @[ x --> F ], f @ F, E `@[ x --> F ], f `@ G, {ptws, F --> f }
  • notation lim is now a definition
  • canonical filtered_prod -> instances using isFiltered.Build, selfFiltered.Build
  • now use set_system and also nbhsType instead of filteredType ...
    • lemmas cvg_ex, cvgP, cvg_toP, dvgP, cvgNpoint, eq_is_cvg
  • canonicals filter_on_eqType, filter_on_choiceType, filter_on_PointedType, filter_on_FilteredType -> instances using gen_eqMixin, gen_choiceMixin, isPointed.Build, isFiltered.Build
  • canonical bool_discrete_filter -> instance using hasNbhs.Build
  • module Topological (packed class) -> mixin Nbhs_isTopological, structure Topological, type topologicalType
    • definition open now a field of the mixin
  • notation continuous now uses definition continuous_at
  • section TopologyOfFilter -> factory Nbhs_isNbhsTopological
  • section TopologyOfOpen -> factory Pointed_isOpenTopological
  • section TopologyOfBase -> factory Pointed_isBaseTopological
  • section TopologyOfSubbase -> factory Pointed_isSubBaseTopological
  • definition Pointed_isSubBaseTopological, canonicals nat_filteredType, nat_topologicalType -> instance using Pointed_isBaseTopological.Build
  • filter now explicit in the notation X --> Y
    • lemmas cvg_addnr, cvg_subnr, cvg_mulnl, cvg_mulnr, cvg_divnr
  • definition prod_topologicalTypeMixin, canonical prod_topologicalType -> instances using hasNbhs.Build, Nbhs_isNbhsTopological.Build
  • definition matrix_topologicalTypeMixin, canonical matrix_topologicalType -> instance using Nbhs_isNbhsTopological.Build
  • definitions weak_topologicalTypeMixin, weak_topologicalType -> instances using Pointed.on, Pointed_isOpenTopological.Build
  • definitions sup_topologicalTypeMixin, sup_topologicalType -> instances using Pointed.on and Pointed_isSubBaseTopological.Build
  • definition product_topologicalType -> definition product_topology_def and instance using Topological.copy
  • in lim_id: nbhs now explicit
  • canonical bool_discrete_topology -> instance using bool_discrete_topology
  • module Uniform (packed class) -> mixin Nbhs_isUniform_mixin, structure Uniform, type uniformType, factories Nbhs_isUniform, isUniform
  • definition prod_uniformType_mixin, canonical prod_uniformType -> instance using Nbhs_isUniform.Build
  • definition matrix_uniformType_mixin, canonical matrix_uniformType -> instance using Nbhs_isUniform.Build
  • definitions weak_uniform_mixin, weak_uniformType -> instance using Nbhs_isUniform.Build
  • definitions fct_uniformType_mixin, fct_topologicalTypeMixin, generic_source_filter, fct_topologicalType, fct_uniformType -> definition arrow_uniform and instance using arrow_uniform
  • definitions sup_uniform_mixin, sup_uniformType -> instance using Nbhs_isUniform.Build
  • definition product_uniformType -> instance using Uniform.copy
  • definition discrete_uniformType -> instance using Choice.on, Choice.on, discrete_uniform_mixin
  • module PseudoMetric (packed class) -> factory Nbhs_isPseudoMetric
  • definition ball now a field of factory Nbhs_isPseudoMetric
  • definition matrix_pseudoMetricType_mixin, canonical matrix_pseudoMetricType -> instance using Uniform_isPseudoMetric.Build
  • definition prod_pseudoMetricType_mixin, canonical prod_pseudoMetricType -> instance using Uniform_isPseudoMetric.Build
  • definition fct_pseudoMetricType_mixin, canonical fct_pseudoMetricType -> instance using Uniform_isPseudoMetric.Build
  • canonical quotient_subtype -> instance using Quotient.copy
  • canonical quotient_eq -> instance using [Sub ... of ... by %/]
  • canonical quotient_choice -> instance using [Choice of ... by <:]
  • canonical quotient_pointed -> instance using isPointed.Build
  • in definition quotient_topologicalType_mixin: topologyOfOpenMixin -> Pointed_isOpenTopological.Build
  • canonical quotient_topologicalType -> instance using quotient_topologicalType_mixin
  • lemma repr_comp_continuous uses the notation \pi_ instead of ... == ... %[mod ...]
  • definition discrete_pseudoMetricType -> instead using discrete_pseudometric_mixin
  • module Complete (packed class) -> mixin Uniform_isComplete, structure Complete, type completeType
    • lemma cauchy_cvg now a mixin field
  • canonical matrix_completeType -> instance using Uniform_isComplete.Build
  • canonical fun_completeType -> instance using Uniform_isComplete.Build
  • module CompletePseudoMetric (packed class) -> structure CompletePseudoMetric
  • matrix instance using Uniform_isComplete.Build
  • function instance using Uniform_isComplete.Build
  • module regular_topology -> instances using Pointed.on, hasNbhs.Build, Nbhs_isPseudoMetric.Build
  • in module numFieldTopology:
    • realType, rcfType, archiFieldType, realFieldType, numClosedFieldType, numFieldType instances using PseudoMetric.copy
  • definition fct_RestrictedUniform, fct_RestrictedUniformTopology, canonical fct_RestrictUniformFilteredType, fct_RestrictUniformTopologicalType, fct_restrictedUniformType -> definition uniform_fun, instance using Unifom.copy for {uniform` _ -> _}
  • definitions fct_Pointwise, fct_PointwiseTopology, canonicals fct_PointwiseFilteredType, fct_PointwiseTopologicalType -> definition pointwise_fun, instance using Topological.copy
  • definition compact_openK_topological_mixin, canonical compact_openK_filter, compact_openK_topological -> instances using Pointed.on, hasNbhs.Build, compact_openK_openE_subproof for compact_openK
  • canonical compact_open_pointedType, definition compact_open_topologicalType, canonicals compact_open_filtered, compact_open_filtered -> definition compact_open_def, instances using Pointed.on, Nbhs.copy, Pointed.on, Nbhs_isTopological
  • definitions weak_pseudoMetricType_mixin, weak_pseudoMetricType -> lemmas weak_pseudo_metric_ball_center, weak_pseudo_metric_entourageE, instance using niform_isPseudoMetric.Build
  • definition countable_uniform_pseudoMetricType_mixin -> module countable_uniform with definition type, instances using Uniform.on, Uniform_isPseudoMetric.Build, lemma countable_uniform_bounded, notation countable_uniform
  • definitions sup_pseudoMetric_mixin, sup_pseudoMetricType, product_pseudoMetricType -> instances using PseudoMetric.on, PseudoMetric.copy
  • definitions subspace_pointedType, subspace_topologicalMixin, canonicals subspace_filteredType, subspace_topologicalType -> instance using Choice.copy, isPointed.Build, hasNbhs.Build, lemmas nbhs_subspaceP_subproof, nbhs_subspace_singleton, nbhs_subspace_nbhs, instance using Nbhs_isNbhsTopological.Build
  • definition subspace_uniformMixin, canonical subspace_uniformType -> instance using Nbhs_isUniform_mixin.Build
  • definition subspace_pseudoMetricType_mixin, canonical subspace_pseudoMetricType -> lemmas subspace_pm_ball_center, subspace_pm_ball_sym, subspace_pm_ball_triangle, subspace_pm_entourageE, instance using Uniform_isPseudoMetric.Build
  • section gauges -> module gauge
    • gauge_pseudoMetricType -> gauge.type (instances using Uniform.on, PseudoMetric.on)
    • gauge_uniformType -> gauge.type

• in cantor.v:

  • in definition tree_of and lemma cantor_like_finite_prod: pointed_discrete -> pointed_discrete_topology

• in normedtype.v:

  • module PseudoMetricNormedZmodule (packed class) -> mixin NormedZmod_PseudoMetric_eq (with field pseudo_metric_ball_norm), structure PseudoMetricNormedZmod
  • now use set_system:
    • definitions pinfty_nbhs, ninfty_nbhs, dominated_by, strictly_dominated_by, bounded_near, sub_klipschitz, lipschitz_on, sub_lipschitz
    • lemmas cvgrnyP, cvgenyP, fcvgrPdist_lt, cvgrPdist_lt, cvgrPdistC_lt, cvgr_dist_lt, cvgr_distC_lt, cvgr_dist_le, cvgr_distC_le, cvgr0Pnorm_lt, cvgr0_norm_lt, cvgr0_norm_le, cvgrPdist_le, cvgrPdist_ltp, cvgrPdist_lep, cvgrPdistC_le, cvgrPdistC_ltp, cvgrPdistC_lep, cvgr0Pnorm_le, cvgr0Pnorm_ltp, cvgr0Pnorm_lep, cvgr_norm_lt, cvgr_norm_le, cvgr_norm_gt, cvgr_norm_ge, cvgr_neq0, real_cvgr_lt, real_cvgr_le, real_cvgr_gt, real_cvgr_ge, cvgr_lt, cvgr_le, cvgr_gt, cvgr_ge, sub_dominatedl, sub_dominatedr, ex_dom_bound, ex_strict_dom_bound, sub_boundedr, sub_boundedl, ex_bound, ex_strict_bound, ex_strict_bound_gt0, klipschitzW, cvg_bounded, fcvgr2dist_ltP, cvgr2dist_ltP, cvgr2dist_lt
  • module NormedModule (packed class) -> mixin PseudoMetricNormedZmod_Lmodule_isNormedModule, structure NormedModule
  • module and section regular_topology -> section regular_topology with instances using Num.NormedZmodule.on, NormedZmod_PseudoMetric_eq.Build, seudoMetricNormedZmod_Lmodule_isNormedModule.Build
  • in module numFieldNormedType
    • realType instances using GRing.ComAlgebra.copy, Vector.copy, NormedModule.copy
    • rcfType instances using GRing.ComAlgebra.copy, Vector.copy, NormedModule.copy
    • archiFieldType instances using GRing.ComAlgebra.copy, Vector.copy, NormedModule.copy
    • realFieldType instances using GRing.ComAlgebra.copy, Vector.copy, NormedModule.copy, Num.RealField.on
    • numClosedFieldType instances using GRing.ComAlgebra.copy, Vector.copy, NormedModule.copy, Num.ClosedField.on
    • numFieldType instances using GRing.ComAlgebra.copy, Vector.copy, NormedModule.copy, Num.NumField.on
  • in lemma norm_lim_id: now explicit use of nbhs
  • definition matrix_PseudoMetricNormedZmodMixin and canonical matrix_normedModType -> instance using PseudoMetricNormedZmod_Lmodule_isNormedModule.Build
  • definition prod_pseudoMetricNormedZmodMixin and canonical prod_normedModType -> instance using PseudoMetricNormedZmod_Lmodule_isNormedModule.Build
  • module CompleteNormedModule (packed class) -> structure CompleteNormedModule
  • canonicals R_regular_completeType, R_regular_CompleteNormedModule -> instance using Uniform_isComplete.Build
  • canonicals R_completeType and R_CompleteNormedModule -> instance using Complete.on
  • now use cvgn instead of cvg:
    • lemma cvg_seq_bounded

• in Rstruct.v:

  • canonicals R_eqMixin, R_eqType -> instance using hasDecEq.Build
  • definition R_choiceMixin and canonical R_choiceType -> instance using hasChoice.Build
  • definition R_zmodMixin and canonical R_zmodType -> instance using isZmodule.Build
  • definition R_ringMixin and canonicals R_ringType, R_comRingType -> instances using Zmodule_isRing.Build, Ring_hasCommutativeMul.Build
  • canonicals Radd_monoid, Radd_comoid -> instance using isComLaw.Build
  • canonicals Rmul_monoid, Rmul_comoid -> instance using isComLaw.Build
  • canonical Rmul_mul_law -> instance using isMulLaw.Build
  • canonical Radd_add_law -> instance using isAddLaw.Build
  • definition R_unitRingMixin and canonical R_unitRing -> instance using Ring_hasMulInverse.Build
  • canonicals R_comUnitRingType and R_idomainType -> instance using ComUnitRing_isIntegral.Build
  • in lemma R_fieldMixin: GRing.Field.mixin_of -> GRing.field_axiom
  • definition Definition and canonical R_fieldType -> instance using UnitRing_isField.Build
  • definition R_numMixin, canonicals R_porderType, R_numDomainType, R_normedZmodType, R_numFieldType -> instance using IntegralDomain_isNumRing.Build
  • in lemma R_total: totalPOrderMixin -> total
  • canonicals R_latticeType, R_distrLatticeType, R_orderType, R_realDomainType, R_realFieldType -> instance using POrder_isTotal.Build
  • in lemmas Rarchimedean_axiom, Rreal_closed_axiom: R_numDomainType -> [the numDomainType of R : Type]
  • canonical R_realArchiFieldType -> instance using RealField_isArchimedean.Build
  • canonical R_rcfType -> instance using RealField_isClosed.Build
  • definition real_realMixin and canonical real_realType -> instance using ArchimedeanField_isReal.Build

• in prodnormedzmodule.v:

  • definition normedZmodMixin and canonical normedZmodType -> instance using Num.Zmodule_isNormed.Build

• in ereal.v:

  • canonical ereal_pointed -> instance using isPointed.Build
  • definitions ereal_dnbhs, ereal_nbhs -> now use set_system
  • canonical ereal_ereal_filter -> instance using hasNbhs.Build
  • definition ereal_topologicalMixin, canonical ereal_topologicalType, definitions ereal_pseudoMetricType_mixin, ereal_uniformType_mixin, canonicals ereal_uniformType, ereal_pseudoMetricType -> instance using Nbhs_isPseudoMetric.Build

• "moved" from normedtype.v to Rstruct.v:

  • canonicals R_pointedType, R_filteredType, R_topologicalType, R_uniformType, R_pseudoMetricType -> instance using PseudoMetric.copy

• in realfun.v:

  • now explicitly display the filter in the notation X --> Y:
    • lemma scvg_at_rightP, cvg_at_leftP, cvge_at_rightP, cvge_at_leftP

• in sequences.v:

  • the lemmas and the notations (in particular, bigop notations) that were using cvg or cvg (... @ \oo)/lim are now using cvgn/limn and now explicitly mention the filter in the notation X --> Y

• in trigo.v:

  • now make explicit mention of the filter:
    • definitions sin, cos
    • lemmas cvg_series_cvg_series_group, lt_sum_lim_series, is_cvg_series_sin_coeff, sinE, cvg_sin_coeff', is_cvg_series_cos_coeff, cosE, cvg_cos_coeff'

• in itv.v:

  • canonical itv_subType -> instance using [isSub for ... ]
  • definitions itv_eqMixin, itv_choiceMixin and canonicals itv_eqType, itv_choiceType -> instance using [Choice of ... by <:]
  • definition itv_porderMixin and canonical itv_porderType -> instance using [SubChoice_isSubPOrder of ... by <: with ...]

• in landau.v:

  • now use set_system
    • structures littleo_type, bigO_type, bigOmega_type, bigTheta_type
    • lemmas littleo_class, littleoE, littleo, bigO_exP, bigO_class, bigO_clone, bigOP, bigOE, bigOmegaP, bigThetaP
    • definitions littleo_clone, the_littleo, littleoP, the_bigO, bigOmega_clone, the_bigOmega, is_bigOmega, bigTheta_clone, is_bigTheta
    • variants littleo_spec, bigOmega_spec, bigTheta_spec
    • notation PhantomF
    • facts is_bigOmega_key, is_bigTheta_key
    • canonicals the_littleo_littleo, the_bigO_bigO, the_littleo_bigO, is_bigOmega_keyed, the_bigOmega_bigOmega, is_bigTheta_keyed, the_bigTheta_bigTheta
  • canonical littleo_subtype -> instance using [isSub for ...]
  • canonical bigO_subtype -> instance using [isSub for ...]
  • in linear_for_continuous:
    • GRing.Scale.op s_law -> GRing.Scale.Law.sort
    • argument s_law removed
  • canonical bigOmega_subtype -> instance using [isSub for ...]
  • canonical bigTheta_subtype -> instance using [isSub for ...]

• in forms.v:

  • module Bilinear (packed class) -> mixin isBilinear, structure Bilinear, definition bilinear_for, factory bilinear_isBilinear, new module Bilinear containing the definition map
  • canonical mulmx_bilinear -> lemma mulmx_is_bilinear and instance using bilinear_isBilinear.Build

• in derive.v

  • in notation 'd, differentiable, is_diff: [filter of ...] -> nbhs F
  • canonical mulr_linear -> instance using isLinear.Build
  • canonical mulr_rev_linear -> instance using isLinear.Build
  • canonical mulr_bilinear -> lemma mulr_is_bilinear and instance using bilinear_isBilinear.Build
  • set (set ...) -> set_system ...

• in esum.v:

  • several occurrences of cvg/lim changed to cvgn/limn and usages of the notation X --> Y changed to X @ F --> Y (with an explicit filter)
    • is_cvg_pseries_inside_norm
    • is_cvg_pseries_inside
    • pseries_diffs_equiv
    • is_cvg_pseries_diffs_equiv
    • pseries_snd_diffs
    • expRE
    • dvg_riemannR

• in numfun.v:

  • canonicals fimfun_mul, fimfun_ring, fimfun_ringType, definition fimfun_ringMixin -> instances using GRing.isMulClosed.Build and [SubZmodule_isSubRing of ... by <:]
  • definition fimfun_comRingMixin, canonical fimfun_comRingType -> instance using [SubRing_isSubComRing of ... by <:]

• in measure.v

  • canonicals salgebraType_eqType, salgebraType_choiceType, salgebraType_ptType -> instance using Pointed.on
  • filter now explicit in:
    • definitions sigma_additive, semi_sigma_additive
    • lemmas nondecreasing_cvg_mu, nonincreasing_cvg_mu
  • canonicals ring_eqType, ring_choiceType, ring_ptType -> instance using Pointed.on

• in lebesgue_measure.v:

  • filter now explicit in lemmas emeasurable_fun_cvg, ae_pointwise_almost_uniform

• in lebesgue_integral.v:

  • canonical mfun_subType -> instance using isSub.Build
  • definitions mfuneqMixin, mfunchoiceMixin, canonicals mfuneqType, mfunchoiceType -> instance using [Choice of ... by <:]
  • canonicals mfun_add, mfun_zmod, mfun_mul, mfun_subring, mfun_zmodType, mfun_ringType, mfun_comRingType, definitions mfun_zmodMixin, mfun_ringMixin, mfun_comRingMixin, -> instances using GRing.isSubringClosed.Build and [SubChoice_isSubComRing of ... <:]
  • canonical sfun_subType -> instance using isSub.Build
  • definitions sfuneqMixin, sfunchoiceMixin, canonicals sfuneqType, sfunchoiceType -> instance using [Choice of .. by <:]
  • canonicals sfun_add, sfun_zmod, sfun_mul, sfun_subring, sfun_zmodType, sfun_ringType, sfun_comRingType, definitions sfun_zmodMixin, sfun_ringMixin, sfun_comRingMixin -> instances using GRing.isSubringClosed.Build and [SubChoice_isSubComRing of ... by <:]
  • now use cvgn/limn instead of cvg/lim:
    • lemmas is_cvg_sintegral, nd_sintegral_lim_lemma, nd_sintegral_lim, nd_ge0_integral_lim, dvg_approx, ecvg_approx
  • filter now explicit in:
    • lemmas approximation, approximation_sfun, cvg_monotone_convergence

• in kernel.v:

  • notation X --> Y changed to X @ F --< Y
    • measurable_fun_xsection_integral
  • definition prob_pointed and canonical probability_ptType -> instance using isPointed.Build
  • canonicals probability_eqType, probability_choiceType -> instance using gen_eqMixin and gen_choiceMixin

• in summability.v:

  • totally now uses set_system

• in altreals/discrete.v:

  • canonical pred_sub_subTypeP -> instance using [isSub for ...]
  • definition pred_sub_eqMixin and canonical pred_sub_eqType -> instance using [Equality of ... by <:]
  • definition pred_sub_choiceMixin and canonical pred_sub_choiceType -> instance using [Choice of ... <:]
  • definition pred_sub_countMixin and pred_sub_countType -> instance using [Countable of ... by <:]
  • definitions countable_countMixin and countable_countType -> countable_countMixin
  • definitions countable_choiceMixin and countable_choiceType -> countable_choiceMixin

• in altreals/xfinmap.v:

  • in lemmas enum_fset0 and enum_fset1: notation [fintype of ...] -> type constraint ... : finType

• in misc/uniform_bigO.v:

  • in definition OuO: [filter of ...] -> nbhs ...

Generalized

• in cantor.v:

  • in definition cantor_space: product_uniformType -> prod_topology
    • instances using Pointed.on, Nbhs.on, Topological.on

• in topology.v:

  • now use nbhsType instead of topologicalType
    • lemma near_fun
    • definition discrete_space
    • definition discrete_uniform_mixin
    • definition discrete_ball, lemma discrete_ball_center, definition discrete_pseudometric_mixin

Removed

• in mathcomp_extra.v:

  • coercion choice.Choice.mixin
  • lemmas bigminr_maxr, definitions AC_subdef, oAC, opACE, canonicals opAC_law, opAC_com_law
  • lemmas some_big_AC, big_ACE, big_undup_AC, perm_big_AC, big_const_idem, big_id_idem, big_mkcond_idem, big_split_idem, big_id_idem_AC, bigID_idem, big_rem_AC, bigD1_AC, sub_big, sub_big_seq, sub_big_seq_cond, uniq_sub_big, uniq_sub_big_cond, sub_big_idem, sub_big_idem_cond, sub_in_big, le_big_ord, subset_big, subset_big_cond, le_big_nat, le_big_ord_cond
  • lemmas bigmax_le, bigmax_lt, lt_bigmin, le_bigmin
  • lemmas bigmax_mkcond, bigmax_split, bigmax_idl, bigmax_idr, bigmaxID
  • lemmas sub_bigmax, sub_bigmax_seq, sub_bigmax_cond, sub_in_bigmax, le_bigmax_nat, le_bigmax_nat_cond, le_bigmax_ord, le_bigmax_ord_cond, subset_bigmax, subset_bigmax_cond
  • lemmas bigmaxD1, le_bigmax_cond, le_bigmax, bigmax_sup, bigmax_leP, bigmax_ltP, bigmax_eq_arg, eq_bigmax, le_bigmax2
  • lemmas bigmin_mkcond, bigmin_split, bigmin_idl, bigmin_idr, bigminID
  • lemmas sub_bigmin, sub_bigmin_cond, sub_bigmin_seq, sub_in_bigmin, le_bigmin_nat, le_bigmin_nat_cond, le_bigmin_ord, le_bigmin_ord_cond, subset_bigmin, subset_bigmin_cond
  • lemmas bigminD1, bigmin_le_cond, bigmin_le, bigmin_inf, bigmin_geP, bigmin_gtP, bigmin_eq_arg, eq_bigmin

• in boolp.v:

  • definitions dep_arrow_eqType, dep_arrow_choiceClass, dep_arrow_choiceType

• in classical_sets.v:

  • notations PointedType, [pointedType of ...]

• in cardinality.v:

  • lemma countable_setT_countMixin

• in constructive_ereal.v:

  • canonicals isLaw.Build, mine_comoid

• in topology.v:

  • structure source, definition source_filter
  • definition filter_of, notation [filter of ...] (now replaced by nbhs), lemma filter_of_filterE
  • definition open_of_nbhs
  • definition open_from, lemma open_fromT
  • canonical eventually_filter_source
  • canonical discrete_topological_mixin
  • canonical set_filter_source
  • definitions filtered_of_normedZmod, pseudoMetric_of_normedDomain
  • definitions fct_UniformFamily (use uniform_fun_family instead), canonicals fct_UniformFamilyFilteredType, fct_UniformFamilyTopologicalType, fct_UniformFamilyUniformType

• in cantor.v:

  • definition pointed_discrete

• in normedtype.v:

  • filtered_of_normedZmod
  • section pseudoMetric_of_normedDomain
    • lemmas ball_norm_center, ball_norm_symmetric, ball_norm_triangle, nbhs_ball_normE
    • definition pseudoMetric_of_normedDomain
  • lemma normrZ
  • canonical matrix_normedZmodType
  • lemmas eq_cvg, eq_is_cvg

• in convex.v:

  • field convexspacechoiceclass, canonicals conv_eqType, conv_choiceType, conv_choiceType

• in measure.v:

  • field ptclass in mixin isSemiRingOfSets
  • canonicals ringOfSets_eqType, ringOfSets_choiceType, ringOfSets_ptType, algebraOfSets_eqType, algebraOfSets_choiceType, algebraOfSets_ptType, measurable_eqType, measurable_choiceType, measurable_ptType
  • field ptclass in factory isAlgebraOfSets
  • field ptclass in factory isMeasurable

• in lebesgue_measure.v:

  • no more "pointed class" argument in definition ereal_isMeasurable

• in lebesgue_stieltjes_measure.v

  • lemma sigmaT_finite_lebesgue_stieltjes_measure turned into a Let

• in altreals/discrete.v:

  • notation [countable of ...]

[0.7.0] - 2024-01-19

Added

• in mathcomp_extra.v:

  • lemmas last_filterP, path_lt_filter0, path_lt_filterT, path_lt_head, path_lt_last_filter, path_lt_le_last

• new file contra.v

  • lemma assume_not
  • tactic assume_not
  • lemma absurd_not
  • tactics absurd_not, contrapose
  • tactic notations contra, contra : constr(H), contra : ident(H), contra : { hyp_list(Hs) } constr(H), contra : { hyp_list(Hs) } ident(H), contra : { - } constr(H)
  • lemma absurd
  • tactic notations absurd, absurd constr(P), absurd : constr(H), absurd : ident(H), absurd : { hyp_list(Hs) } constr(H), absurd : { hyp_list(Hs) } ident(H)

• in topology.v:

  • lemma filter_bigI_within
  • lemma near_powerset_map
  • lemma near_powerset_map_monoE
  • lemma fst_open
  • lemma snd_open
  • definition near_covering_within
  • lemma near_covering_withinP
  • lemma compact_setM
  • lemma compact_regular
  • lemma fam_compact_nbhs
  • definition compact_open, notation {compact-open, U -> V}
  • notation {compact-open, F --> f}
  • definition compact_openK
  • definition compact_openK_nbhs
  • instance compact_openK_nbhs_filter
  • definition compact_openK_topological_mixin
  • canonicals compact_openK_filter, compact_openK_topological, compact_open_pointedType
  • definition compact_open_topologicalType
  • canonicals compact_open_filtered, compact_open_topological
  • lemma compact_open_cvgP
  • lemma compact_open_open
  • lemma compact_closedI
  • lemma compact_open_fam_compactP
  • lemma compact_equicontinuous
  • lemma uniform_regular
  • lemma continuous_curry
  • lemma continuous_uncurry_regular
  • lemma continuous_uncurry
  • lemma curry_continuous
  • lemma uncurry_continuous

• in ereal.v:

  • lemma ereal_supy

• in file normedtype.v,

  • new lemma continuous_within_itvP.

• in file realfun.v,

  • definitions itv_partition, itv_partitionL, itv_partitionR, variation, variations, bounded_variation, total_variation, neg_tv, and pos_tv.

  • new lemmas left_right_continuousP, nondecreasing_funN, nonincreasing_funN

  • new lemmas itv_partition_nil, itv_partition_cons, itv_partition1, itv_partition_size_neq0, itv_partitionxx, itv_partition_le, itv_partition_cat, itv_partition_nth_size, itv_partition_nth_ge, itv_partition_nth_le, nondecreasing_fun_itv_partition, nonincreasing_fun_itv_partition, itv_partitionLP, itv_partitionRP, in_itv_partition, notin_itv_partition, itv_partition_rev,

  • new lemmas variation_zip, variation_prev, variation_next, variation_nil, variation_ge0, variationN, variation_le, nondecreasing_variation, nonincreasing_variation, variationD, variation_itv_partitionLR, le_variation, variation_opp_rev, variation_rev_opp

  • new lemmas variations_variation, variations_neq0, variationsN, variationsxx

  • new lemmas bounded_variationxx, bounded_variationD, bounded_variationN, bounded_variationl, bounded_variationr, variations_opp, nondecreasing_bounded_variation

  • new lemmas total_variationxx, total_variation_ge, total_variation_ge0, bounded_variationP, nondecreasing_total_variation, total_variationN, total_variation_le, total_variationD, neg_tv_nondecreasing, total_variation_pos_neg_tvE, fine_neg_tv_nondecreasing, neg_tv_bounded_variation, total_variation_right_continuous, neg_tv_right_continuous, total_variation_opp, total_variation_left_continuous, total_variation_continuous

• in lebesgue_stieltjes_measure.v:

  • sigma_finite_measure HB instance on lebesgue_stieltjes_measure

• in lebesgue_measure.v:

  • sigma_finite_measure HB instance on lebesgue_measure

• in lebesgue_integral.v:

  • sigma_finite_measure instance on product measure \x

Changed

• in topology.v:
  • lemmas nbhsx_ballx and near_ball take a parameter of type R instead of {posnum R}
  • lemma pointwise_compact_cvg

Generalized

• in realfun.v:

  • lemmas nonincreasing_at_right_cvgr, nonincreasing_at_left_cvgr
  • lemmas nondecreasing_at_right_cvge, nondecreasing_at_right_is_cvge, nonincreasing_at_right_cvge, nonincreasing_at_right_is_cvge

• in realfun.v:

  • lemmas nonincreasing_at_right_is_cvgr, nondecreasing_at_right_is_cvgr

[0.6.7] - 2024-01-09

Added

• in boolp.v:

  • tactic eqProp
  • variant BoolProp
  • lemmas PropB, notB, andB, orB, implyB, decide_or, not_andE, not_orE, orCA, orAC, orACA, orNp, orpN, or3E, or4E, andCA, andAC, andACA, and3E, and4E, and5E, implyNp, implypN, implyNN, or_andr, or_andl, and_orr, and_orl, exists2E, inhabitedE, inhabited_witness

• in topology.v,

  • new lemmas perfect_set2, and ent_closure.
  • lemma clopen_surj
  • lemma nbhs_dnbhs_neq
  • lemma dnbhs_ball

• in constructive_ereal.v

  • lemma lee_subgt0Pr

• in ereal.v:

  • lemmas ereal_sup_le, ereal_inf_le

• in normedtype.v:

  • hints for at_right_proper_filter and at_left_proper_filter
  • definition lower_semicontinuous
  • lemma lower_semicontinuousP
  • lemma not_near_at_rightP
  • lemmas withinN, at_rightN, at_leftN, cvg_at_leftNP, cvg_at_rightNP
  • lemma dnbhsN
  • lemma limf_esup_dnbhsN
  • definitions limf_esup, limf_einf
  • lemmas limf_esupE, limf_einfE, limf_esupN, limf_einfN

• in sequences.v:

  • lemma minr_cvg_0_cvg_0
  • lemma mine_cvg_0_cvg_fin_num
  • lemma mine_cvg_minr_cvg
  • lemma mine_cvg_0_cvg_0
  • lemma maxr_cvg_0_cvg_0
  • lemma maxe_cvg_0_cvg_fin_num
  • lemma maxe_cvg_maxr_cvg
  • lemma maxe_cvg_0_cvg_0
  • lemmas limn_esup_lim, limn_einf_lim

• in file cantor.v,

  • definitions cantor_space, cantor_like, pointed_discrete, and tree_of.
  • new lemmas cantor_space_compact, cantor_space_hausdorff, cantor_zero_dimensional, cantor_perfect, cantor_like_cantor_space, tree_map_props, homeomorphism_cantor_like, and cantor_like_finite_prod.
  • new theorem cantor_surj.

• in numfun.v:

  • lemma patch_indic

• in realfun.v:

  • notations nondecreasing_fun, nonincreasing_fun, increasing_fun, decreasing_fun
  • lemmas cvg_addrl, cvg_addrr, cvg_centerr, cvg_shiftr, nondecreasing_cvgr, nonincreasing_at_right_cvgr, nondecreasing_at_right_cvgr, nondecreasing_cvge, nondecreasing_is_cvge, nondecreasing_at_right_cvge, nondecreasing_at_right_is_cvge, nonincreasing_at_right_cvge, nonincreasing_at_right_is_cvge
  • lemma cvg_at_right_left_dnbhs
  • lemma cvg_at_rightP
  • lemma cvg_at_leftP
  • lemma cvge_at_rightP
  • lemma cvge_at_leftP
  • lemma lime_sup
  • lemma lime_inf
  • lemma lime_supE
  • lemma lime_infE
  • lemma lime_infN
  • lemma lime_supN
  • lemma lime_sup_ge0
  • lemma lime_inf_ge0
  • lemma lime_supD
  • lemma lime_sup_le
  • lemma lime_inf_sup
  • lemma lim_lime_inf
  • lemma lim_lime_sup
  • lemma lime_sup_inf_at_right
  • lemma lime_sup_inf_at_left
  • lemmas lime_sup_lim, lime_inf_lim

• in file measure.v

  • add lemmas ae_eq_subset, measure_dominates_ae_eq.

• in lebesgue_measure.v

  • lemma lower_semicontinuous_measurable

• in lebesgue_integral.v:

  • definition locally_integrable
  • lemmas integrable_locally, locally_integrableN, locally_integrableD, locally_integrableB
  • definition iavg
  • lemmas iavg0, iavg_ge0, iavg_restrict, iavgD
  • definitions HL_maximal
  • lemmas HL_maximal_ge0, HL_maximalT_ge0, lower_semicontinuous_HL_maximal, measurable_HL_maximal, maximal_inequality

• in charge.v

  • definition charge_of_finite_measure (instance of charge)
  • lemmas dominates_cscalel, dominates_cscaler
  • definition cpushforward (instance of charge)
  • lemma dominates_pushforward
  • lemma cjordan_posE
  • lemma jordan_posE
  • lemma cjordan_negE
  • lemma jordan_negE
  • lemma Radon_Nikodym_sigma_finite
  • lemma Radon_Nikodym_fin_num
  • lemma Radon_Nikodym_integral
  • lemma ae_eq_Radon_Nikodym_SigmaFinite
  • lemma Radon_Nikodym_change_of_variables
  • lemma Radon_Nikodym_cscale
  • lemma Radon_Nikodym_cadd
  • lemma Radon_Nikodym_chain_rule

Changed

• in boolp.v

  • lemmas orC and andC now use commutative

• moved from topology.v to mathcomp_extra.v

  • definition monotonous

• in normedtype.v:

  • lemmas vitali_lemma_finite and vitali_lemma_finite_cover now returns duplicate-free lists of indices

• in sequences.v:

  • change the implicit arguments of trivIset_seqDU
  • limn_esup now defined from lime_sup
  • limn_einf now defined from limn_esup

• moved from lebesgue_integral.v to measure.v:

  • definition ae_eq
  • lemmas ae_eq0, ae_eq_comp, ae_eq_funeposneg, ae_eq_refl, ae_eq_trans, ae_eq_sub, ae_eq_mul2r, ae_eq_mul2l, ae_eq_mul1l, ae_eq_abse

• in charge.v

  • definition jordan_decomp now uses cadd and cscale
  • definition Radon_Nikodym_SigmaFinite now in a module Radon_Nikodym_SigmaFinite with
    • definition f
    • lemmas f_ge0, f_fin_num, f_integrable, f_integral
    • lemma change_of_variables
    • lemma integralM
    • lemma chain_rule

Renamed

• in exp.v:

  • lnX -> lnXn

• in charge.v:

  • dominates_caddl -> dominates_cadd

Generalized

• in lebesgue_measure.v

  • an hypothesis of lemma integral_ae_eq is weakened

• in lebesgue_integral.v

  • ge0_integral_bigsetU generalized from nat to eqType

Removed

• in boolp.v:

  • lemma pdegen

• in forms.v:

  • lemmas eq_map_mx, map_mx_id

[0.6.6] - 2023-11-14

Added

• in mathcomp_extra.v

  • lemmas ge0_ler_normr, gt0_ler_normr, le0_ger_normr and lt0_ger_normr
  • lemma leq_ltn_expn
  • lemma onemV

• in classical_sets.v:

  • lemma set_cons1
  • lemma trivIset_bigcup
  • definition maximal_disjoint_subcollection
  • lemma ex_maximal_disjoint_subcollection
  • lemmas mem_not_I, trivIsetT_bigcup

• in constructive_ereal.v:

  • lemmas gt0_fin_numE, lt0_fin_numE
  • lemmas le_er_map, er_map_idfun

• in reals.v:

  • lemma le_inf
  • lemmas ceilN, floorN

• in topology.v:

  • lemmas closure_eq0, separated_open_countable

• in normedtype.v:

  • lemmas ball0, ball_itv, closed_ball0, closed_ball_itv
  • definitions cpoint, radius, is_ball
  • definition scale_ball, notation notation *`
  • lemmas sub_scale_ball, scale_ball1, sub1_scale_ball
  • lemmas ball_inj, radius0, cpoint_ball, radius_ball_num, radius_ball, is_ballP, is_ball_ball, scale_ball_set0, ballE, is_ball_closure, scale_ballE, cpoint_scale_ball, radius_scale_ball
  • lemmas vitali_lemma_finite, vitali_lemma_finite_cover
  • definition vitali_collection_partition
  • lemmas vitali_collection_partition_ub_gt0, ex_vitali_collection_partition, cover_vitali_collection_partition, disjoint_vitali_collection_partition
  • lemma separate_closed_ball_countable
  • lemmas vitali_lemma_infinite, vitali_lemma_infinite_cover
  • lemma open_subball
  • lemma closed_disjoint_closed_ball
  • lemma is_scale_ball
  • lemmas scale_ball0, closure_ball, bigcup_ballT

• in sequences.v:

  • lemma nneseries_tail_cvg

• in exp.v:

  • definition expeR
  • lemmas expeR0, expeR_ge0, expeR_gt0
  • lemmas expeR_eq0, expeRD, expeR_ge1Dx
  • lemmas ltr_expeR, ler_expeR, expeR_inj, expeR_total
  • lemmas mulr_powRB1, fin_num_poweR, poweRN, poweR_lty, lty_poweRy, gt0_ler_poweR
  • lemma expRM

• in measure.v:

  • lemmas negligibleI, negligible_bigsetU, negligible_bigcup
  • lemma probability_setC
  • lemma measure_sigma_sub_additive_tail
  • lemma outer_measure_sigma_subadditive_tail

• new lebesgue_stieltjes_measure.v:

  • notation right_continuous
  • lemmas right_continuousW, nondecreasing_right_continuousP
  • mixin isCumulative, structure Cumulative, notation cumulative
  • idfun instance of Cumulative
  • wlength, wlength0, wlength_singleton, wlength_setT, wlength_itv, wlength_finite_fin_num, finite_wlength_itv, wlength_itv_bnd, wlength_infty_bnd, wlength_bnd_infty, infinite_wlength_itv, wlength_itv_ge0, wlength_Rhull, le_wlength_itv, le_wlength, wlength_semi_additive, wlength_ge0, lebesgue_stieltjes_measure_unique
  • content instance of hlength
  • cumulative_content_sub_fsum, wlength_sigma_sub_additive, wlength_sigma_finite
  • measure instance of hlength
  • definition lebesgue_stieltjes_measure

• in lebesgue_measure.v:

  • lemma lebesgue_measurable_ball
  • lemmas measurable_closed_ball, lebesgue_measurable_closed_ball
  • definition vitali_cover
  • lemma vitali_theorem

• in lebesgue_integral.v:

  • mfun instances for expR and comp
  • lemma abse_integralP

• in charge.v:

  • factory isCharge
  • Notations .-negative_set, .-positive_set
  • lemmas dominates_cscale, Radon_Nikodym_cscale
  • definition cadd, lemmas dominates_caddl, Radon_Nikodym_cadd

• in probability.v:

  • definition mmt_gen_fun, chernoff

• in hoelder.v:

  • lemmas powR_Lnorm, minkowski

Changed

• in normedtype.v:

  • order of arguments of squeeze_cvgr

• moved from derive.v to normedtype.v:

  • lemmas cvg_at_rightE, cvg_at_leftE

• in measure.v:

  • order of parameters changed in semi_sigma_additive_is_additive, isMeasure

• in lebesgue_measure.v:

  • are now prefixed with LebesgueMeasure:
    • hlength, hlength0, hlength_singleton, hlength_setT, hlength_itv, hlength_finite_fin_num, hlength_infty_bnd, hlength_bnd_infty, hlength_itv_ge0, hlength_Rhull, le_hlength_itv, le_hlength, hlength_ge0, hlength_semi_additive, hlength_sigma_sub_additive, hlength_sigma_finite, lebesgue_measure
    • finite_hlengthE renamed to finite_hlentgh_itv
    • pinfty_hlength renamed to infinite_hlength_itv
  • lebesgue_measure now defined with lebesgue_stieltjes_measure
  • lebesgue_measure_itv does not refer to hlength anymore
  • remove one argument of lebesgue_regularity_inner_sup

• moved from lebesgue_measure.v to lebesgue_stieltjes_measure.v

  • notations _.-ocitv, _.-ocitv.-measurable
  • definitions ocitv, ocitv_display
  • lemmas is_ocitv, ocitv0, ocitvP, ocitvD, ocitvI

• in lebesgue_integral.v:

  • integral_dirac now uses the \d_ notation
  • order of arguments in the lemma le_abse_integral

• in hoelder.v:

  • definition Lnorm now HB.locked

• in probability.v:

  • markov now uses Num.nneg

Renamed

• in ereal.v:

  • le_er_map -> le_er_map_in

• in sequences.v:

  • lim_sup -> limn_sup
  • lim_inf -> limn_inf
  • lim_infN -> limn_infN
  • lim_supE -> limn_supE
  • lim_infE -> limn_infE
  • lim_inf_le_lim_sup -> limn_inf_sup
  • cvg_lim_inf_sup -> cvg_limn_inf_sup
  • cvg_lim_supE -> cvg_limn_supE
  • le_lim_supD -> le_limn_supD
  • le_lim_infD -> le_limn_infD
  • lim_supD -> limn_supD
  • lim_infD -> limn_infD
  • LimSup.lim_esup -> limn_esup
  • LimSup.lim_einf -> limn_einf
  • lim_einf_shift -> limn_einf_shift
  • lim_esup_le_cvg -> limn_esup_le_cvg
  • lim_einfN -> limn_einfN
  • lim_esupN -> limn_esupN
  • lim_einf_sup -> limn_einf_sup
  • cvgNy_lim_einf_sup -> cvgNy_limn_einf_sup
  • cvg_lim_einf_sup -> cvg_limn_einf_sup
  • is_cvg_lim_einfE -> is_cvg_limn_einfE
  • is_cvg_lim_esupE -> is_cvg_limn_esupE
  • ereal_nondecreasing_cvg -> ereal_nondecreasing_cvgn
  • ereal_nondecreasing_is_cvg -> ereal_nondecreasing_is_cvgn
  • ereal_nonincreasing_cvg -> ereal_nonincreasing_cvgn
  • ereal_nonincreasing_is_cvg -> ereal_nonincreasing_is_cvgn
  • ereal_nondecreasing_opp -> ereal_nondecreasing_oppn
  • nonincreasing_cvg_ge -> nonincreasing_cvgn_ge
  • nondecreasing_cvg_le -> nondecreasing_cvgn_le
  • nonincreasing_cvg -> nonincreasing_cvgn
  • nondecreasing_cvg -> nondecreasing_cvgn
  • nonincreasing_is_cvg -> nonincreasing_is_cvgn
  • nondecreasing_is_cvg -> nondecreasing_is_cvgn
  • near_nonincreasing_is_cvg -> near_nonincreasing_is_cvgn
  • near_nondecreasing_is_cvg -> near_nondecreasing_is_cvgn
  • nondecreasing_dvg_lt -> nondecreasing_dvgn_lt

• in lebesgue_measure.v:

  • measurable_fun_lim_sup -> measurable_fun_limn_sup
  • measurable_fun_lim_esup -> measurable_fun_limn_esup

• in charge.v

  • isCharge -> isSemiSigmaAdditive

Generalized

• in classical_sets.v:

  • set_nil generalized to eqType

• in topology.v:

  • ball_filter generalized to realDomainType

• in lebesgue_integral.v:

  • weaken an hypothesis of integral_ae_eq

Removed

• lebesgue_measure_unique (generalized to lebesgue_stieltjes_measure_unique)

• in sequences.v:

  • notations elim_sup, elim_inf
  • LimSup.lim_esup, LimSup.lim_einf
  • elim_inf_shift
  • elim_sup_le_cvg
  • elim_infN
  • elim_supN
  • elim_inf_sup
  • cvg_ninfty_elim_inf_sup
  • cvg_ninfty_einfs
  • cvg_ninfty_esups
  • cvg_pinfty_einfs
  • cvg_pinfty_esups
  • cvg_elim_inf_sup
  • is_cvg_elim_infE
  • is_cvg_elim_supE

• in lebesgue_measure.v:

  • measurable_fun_elim_sup

[0.6.5] - 2023-10-02

Added

• in mathcomp_extra.v:
  • lemmas le_bigmax_seq, bigmax_sup_seq
  • lemma gerBl
• in classical_sets.v:
  • lemma setU_id2r
• in ereal.v:
  • lemmas uboundT, supremumsT, supremumT, ereal_supT, range_oppe, ereal_infT
• in constructive_ereal.v:
  • lemma eqe_pdivr_mull
  • lemma bigmaxe_fin_num
• in file topology.v,
  • definition regular_space.
  • lemma ent_closure.
• in normedtype.v:
  • lemmas open_itvoo_subset, open_itvcc_subset
  • new lemmas normal_openP, uniform_regular, regular_openP, and pseudometric_normal.
• in sequences.v:
  • lemma cvge_harmonic
• in convex.v:
  • lemmas conv_gt0, convRE
  • definition convex_function
• in exp.v:
  • lemmas concave_ln, conjugate_powR
  • lemmas ln_le0, ger_powR, ler1_powR, le1r_powR, ger1_powR, ge1r_powR, ge1r_powRZ, le1r_powRZ
  • lemma gt0_ltr_powR
  • lemma powR_injective
• in measure.v:
  • lemmas outer_measure_subadditive, outer_measureU2
  • definition ess_sup, lemma ess_sup_ge0
• in lebesgue_measure.v:
  • lemma compact_measurable
  • declare lebesgue_measure as a SigmaFinite instance
  • lemma lebesgue_regularity_inner_sup
  • lemma measurable_ball
  • lemma measurable_mulrr
• in lebesgue_integral.v,
  • new lemmas integral_le_bound, continuous_compact_integrable, and lebesgue_differentiation_continuous.
  • new lemmas simple_bounded, measurable_bounded_integrable, compact_finite_measure, approximation_continuous_integrable
  • lemma ge0_integral_count
• in kernel.v:
  • kseries is now an instance of Kernel_isSFinite_subdef
• new file hoelder.v:
  • definition Lnorm, notations 'N[mu]_p[f], 'N_p[f]
  • lemmas Lnorm1, Lnorm_ge0, eq_Lnorm, Lnorm_eq0_eq0
  • lemma hoelder
  • lemmas Lnorm_counting, hoelder2, convex_powR

Changed

• in cardinality.v:
  • implicits of fimfunP
• in constructive_ereal.v:
  • lee_adde renamed to lee_addgt0Pr and turned into a reflect
  • lee_dadde renamed to lee_daddgt0Pr and turned into a reflect
• in exp.v:
  • gt0_ler_powR now uses Num.nneg
• removed dependency in Rstruct.v on normedtype.v:
• added dependency in normedtype.v on Rstruct.v:
• mnormalize moved from kernel.v to measure.v and generalized
• in measure.v:
  • implicits of measurable_fst and measurable_snd
• in lebesgue_integral.v
  • rewrote negligible_integral to replace the positivity condition with an integrability condition, and added ge0_negligible_integral.
  • implicits of integral_le_bound

Renamed

• in constructive_ereal.v:
  • lee_opp -> leeN2
  • lte_opp -> lteN2
• in normedtype.v:
  • normal_urysohnP -> normal_separatorP.
• in exp.v:
  • gt0_ler_powR -> ge0_ler_powR

Removed

• in signed.v:
  • specific notation for 2%:R, now subsumed by number notations in MC >= 1.15 Note that when importing ssrint, 2 now denotes 2%:~R rather than 2%:R, which are convertible but don't have the same head constant.

[0.6.4] - 2023-08-05

Added

• in theories/Make
  • file probability.v (wasn't compiled in OPAM packages up to now)
• in mathcomp_extra.v:
  • definition min_fun, notation \min
  • new lemmas maxr_absE, minr_absE
• in file boolp.v,
  • lemmas notP, notE
  • new lemma implyE.
  • new lemmas contra_leP and contra_ltP
• in classical_sets.v:
  • lemmas set_predC, preimage_true, preimage_false
  • lemmas properW, properxx
  • lemma Zorn_bigcup
  • lemmas imsub1 and imsub1P
  • lemma bigcup_bigcup
• in constructive_ereal.v:
  • lemmas lte_pmulr, lte_pmull, lte_nmulr, lte_nmull
  • lemmas lte0n, lee0n, lte1n, lee1n
  • lemmas fine0 and fine1
• in file reals.v:
  • lemmas sup_sumE, inf_sumE
• in signed.v:
  • lemmas Posz_snum_subproof and Negz_snum_subproof
  • canonical instances Posz_snum and Negz_snum
• in file topology.v,
  • new lemma uniform_nbhsT.
  • definition set_nbhs.
  • new lemmas filterI_iter_sub, filterI_iterE, finI_fromI, filterI_iter_finI, smallest_filter_finI, and set_nbhsP.
  • lemma bigsetU_compact
  • lemma ball_symE
  • new lemma pointwise_cvgP.
  • lemma closed_bigcup
  • definition normal_space.
  • new lemmas filter_inv, and countable_uniform_bounded.
• in file normedtype.v,
  • definition edist.
  • lemmas edist_ge0, edist_neqNy, edist_lt_ball, edist_fin, edist_pinftyP, edist_finP, edist_fin_open, edist_fin_closed, edist_pinfty_open, edist_sym, edist_triangle, edist_continuous, edist_closeP, and edist_refl.
  • definitions edist_inf, uniform_separator, and Urysohn.
  • lemmas continuous_min, continuous_max, edist_closel, edist_inf_ge0, edist_inf_neqNy, edist_inf_triangle, edist_inf_continuous, edist_inf0, Urysohn_continuous, Urysohn_range, Urysohn_sub0, Urysohn_sub1, Urysohn_eq0, Urysohn_eq1, uniform_separatorW, normal_uniform_separator, uniform_separatorP, normal_urysohnP, and subset_closure_half.
• in file real_interval.v,
  • new lemma bigcup_itvT.
• in sequences.v:
  • lemma eseries_cond
  • lemmas eseries_mkcondl, eseries_mkcondr
  • new lemmas geometric_partial_tail, and geometric_le_lim.
• in exp.v:
  • lemmas powRrM, gt0_ler_powR, gt0_powR, norm_powR, lt0_norm_powR, powRB
  • lemmas poweRrM, poweRAC, gt0_poweR, poweR_eqy, eqy_poweR, poweRD, poweRB
  • notation e `^?(r +? s)
  • lemmas expR_eq0, powRN
  • definition poweRD_def
  • lemmas poweRD_defE, poweRB_defE, add_neq0_poweRD_def, add_neq0_poweRB_def, nneg_neq0_poweRD_def, nneg_neq0_poweRB_def
  • lemmas powR_eq0, poweR_eq0
• in file numfun.v,
  • new lemma continuous_bounded_extension.
• in measure.v:
  • lemma lebesgue_regularity_outer
  • new lemmas measureU0, nonincreasing_cvg_mu, and epsilon_trick0.
  • new lemmas finite_card_sum, and measureU2.
• in lebesgue_measure.v:
  • lemma closed_measurable
  • new lemmas lebesgue_nearly_bounded, and lebesgue_regularity_inner.
  • new lemmas pointwise_almost_uniform, and ae_pointwise_almost_uniform.
  • lemmas measurable_fun_ltr, measurable_minr
• in file lebesgue_integral.v,
  • new lemmas lusin_simple, and measurable_almost_continuous.
  • new lemma approximation_sfun_integrable.

Changed

• in classical_sets.v:

  • bigcup_bigcup_dep renamed to bigcup_setM_dep and equality in the statement reversed
  • bigcup_bigcup renamed to bigcup_setM and equality in the statement reversed

• in sequences.v:

  • lemma nneseriesrM generalized and renamed to nneseriesZl

• in exp.v:

  • lemmas power_posD (now powRD), power_posB (now powRB)

• moved from lebesgue_measure.v to real_interval.v:

  • lemmas set1_bigcap_oc, itv_bnd_open_bigcup, itv_open_bnd_bigcup, itv_bnd_infty_bigcup, itv_infty_bnd_bigcup

• moved from functions.v to classical_sets.v: subsetP.

• moved from normedtype.v to topology.v: Rhausdorff.

Renamed

• in boolp.v:
  • mextentionality -> mextensionality
  • extentionality -> extensionality
• in classical_sets.v:
  • bigcup_set_cond -> bigcup_seq_cond
  • bigcup_set -> bigcup_seq
  • bigcap_set_cond -> bigcap_seq_cond
  • bigcap_set -> bigcap_seq
• in normedtype.v:
  • nbhs_closedballP -> nbhs_closed_ballP
• in exp.v:
  • expK -> expRK
  • power_pos_eq0 -> powR_eq0_eq0
  • power_pos_inv -> powR_invn
  • powere_pos_eq0 -> poweR_eq0_eq0
  • power_pos -> powR
  • power_pos_ge0 -> powR_ge0
  • power_pos_gt0 -> powR_gt0
  • gt0_power_pos -> gt0_powR
  • power_pos0 -> powR0
  • power_posr1 -> powRr1
  • power_posr0 -> powRr0
  • power_pos1 -> powR1
  • ler_power_pos -> ler_powR
  • gt0_ler_power_pos -> gt0_ler_powR
  • power_posM -> powRM
  • power_posrM -> powRrM
  • power_posAC -> powRAC
  • power_posD -> powRD
  • power_posN -> powRN
  • power_posB -> powRB
  • power_pos_mulrn -> powR_mulrn
  • power_pos_inv1 -> powR_inv1
  • power_pos_intmul -> powR_intmul
  • ln_power_pos -> ln_powR
  • power12_sqrt -> powR12_sqrt
  • norm_power_pos -> norm_powR
  • lt0_norm_power_pos -> lt0_norm_powR
  • powere_pos -> poweR
  • powere_pos_EFin -> poweR_EFin
  • powere_posyr -> poweRyr
  • powere_pose0 -> poweRe0
  • powere_pose1 -> poweRe1
  • powere_posNyr -> poweRNyr
  • powere_pos0r -> poweR0r
  • powere_pos1r -> poweR1r
  • fine_powere_pos -> fine_poweR
  • powere_pos_ge0 -> poweR_ge0
  • powere_pos_gt0 -> poweR_gt0
  • powere_posM -> poweRM
  • powere12_sqrt -> poweR12_sqrt
• in lebesgue_measure.v:
  • measurable_power_pos -> measurable_powR
• in lebesgue_integral.v:
  • ge0_integralM_EFin -> ge0_integralZl_EFin
  • ge0_integralM -> ge0_integralZl
  • integralM_indic -> integralZl_indic
  • integralM_indic_nnsfun -> integralZl_indic_nnsfun
  • integrablerM -> integrableZl
  • integrableMr -> integrableZr
  • integralM -> integralZl

Generalized

• in sequences.v:
  • lemmas is_cvg_nneseries_cond, is_cvg_npeseries_cond
  • lemmas is_cvg_nneseries, is_cvg_npeseries
  • lemmas nneseries_ge0, npeseries_le0
  • lemmas eq_eseriesr, lee_nneseries
• in exp.v:
  • lemmas convex_expR, ler_power_pos (now ler_powR)
  • lemma ln_power_pos (now ln_powR)
  • lemma ln_power_pos
• in measure.v:
  • lemmas measureDI, measureD, measureUfinl, measureUfinr, null_set_setU, measureU0 (from measure to content)
  • lemma subset_measure0 (from realType to realFieldType)
• in file lebesgue_integral.v, updated le_approx.

Removed

• in topology.v:
  • lemma my_ball_le (use ball_le instead)
• in signed.v:
  • lemma nat_snum_subproof
  • canonical instance nat_snum (useless, there is already a default instance pointing to the typ_snum mechanism (then identifying nats as >= 0))

[0.6.3] - 2023-06-21

Added

• in mathcomp_extra.v
  • definition coefE (will be in MC 2.1/1.18)
  • lemmas deg2_poly_canonical, deg2_poly_factor, deg2_poly_min, deg2_poly_minE, deg2_poly_ge0, Real.deg2_poly_factor, deg_le2_poly_delta_ge0, deg_le2_poly_ge0 (will be in MC 2.1/1.18)
  • lemma deg_le2_ge0
• in classical_sets.v:
  • lemmas set_eq_le, set_neq_lt,
  • new lemma trivIset1.
  • lemmas preimage_mem_true, preimage_mem_false
• in functions.v:
  • lemma sumrfctE
• in set_interval.v:
  • lemma set_lte_bigcup
• in topology.v:
  • lemma globally0
  • definitions basis, and second_countable.
  • lemmas clopen_countable and compact_countable_base.
• in ereal.v:
  • lemmas compreDr, compreN
• in constructive_ereal.v:
  • lemmas lee_sqr, lte_sqr, lee_sqrE, lte_sqrE, sqre_ge0, EFin_expe, sqreD, sqredD
• in normedtype.v:
  • lemma lipschitz_set0, lipschitz_set1
• in sequences.v:
  • lemma eq_eseriesl
• in measure.v:
  • new lemmas measurable_subring, and semiring_sigma_additive.
  • added factory Content_SubSigmaAdditive_isMeasure
  • lemma measurable_fun_bigcup
  • definition measure_dominates, notation `<<
  • lemma measure_dominates_trans
  • defintion mfrestr
  • lemmas measurable_pair1, measurable_pair2
• in lebesgue_measure.v:
  • lemma measurable_expR
• in lebesgue_integral.v:
  • lemmas emeasurable_fun_lt, emeasurable_fun_le, emeasurable_fun_eq, emeasurable_fun_neq
  • lemma integral_ae_eq
  • lemma integrable_sum
  • lemmas integrableP, measurable_int
• in file kernel.v,
  • definitions kseries, measure_fam_uub, kzero, kdirac, prob_pointed, mset, pset, pprobability, kprobability, kadd, mnormalize, knormalize, kcomp, and mkcomp.
  • lemmas eq_kernel, measurable_fun_kseries, integral_kseries, measure_fam_uubP, eq_sfkernel, kzero_uub, sfinite_kernel, sfinite_kernel_measure, finite_kernel_measure, measurable_prod_subset_xsection_kernel, measurable_fun_xsection_finite_kernel, measurable_fun_xsection_integral, measurable_fun_integral_finite_kernel, measurable_fun_integral_sfinite_kernel, lt0_mset, gt1_mset, kernel_measurable_eq_cst, kernel_measurable_neq_cst, kernel_measurable_fun_eq_cst, measurable_fun_kcomp_finite, mkcomp_sfinite, measurable_fun_mkcomp_sfinite, measurable_fun_preimage_integral, measurable_fun_integral_kernel, and integral_kcomp.
  • lemma measurable_fun_mnormalize
• in probability.v
  • definition of covariance
  • lemmas expectation_sum, covarianceE, covarianceC, covariance_fin_num, covariance_cst_l, covariance_cst_r, covarianceZl, covarianceZr, covarianceNl, covarianceNr, covarianceNN, covarianceDl, covarianceDr, covarianceBl, covarianceBr, variance_fin_num, varianceZ, varianceN, varianceD, varianceB, varianceD_cst_l, varianceD_cst_r, varianceB_cst_l, varianceB_cst_r
  • lemma covariance_le
  • lemma cantelli
• in charge.v:
  • definition measure_of_charge
  • definition crestr0
  • definitions jordan_neg, jordan_pos
  • lemmas jordan_decomp, jordan_pos_dominates, jordan_neg_dominates
  • lemma radon_nikodym_finite
  • definition Radon_Nikodym, notation 'd nu '/d mu
  • theorems Radon_Nikodym_integrable, Radon_Nikodym_integral

Changed

• in lebesgue_measure.v
  • measurable_funrM, measurable_funN, measurable_fun_exprn
• in lebesgue_integral.v:
  • lemma xsection_ndseq_closed generalized from a measure to a family of measures
  • locked integrable and put it in bool rather than Prop
• in probability.v
  • variance is now defined based on covariance

Renamed

• in derive.v:
  • Rmult_rev -> mulr_rev
  • rev_Rmult -> rev_mulr
  • Rmult_is_linear -> mulr_is_linear
  • Rmult_linear -> mulr_linear
  • Rmult_rev_is_linear -> mulr_rev_is_linear
  • Rmult_rev_linear -> mulr_rev_linear
  • Rmult_bilinear -> mulr_bilinear
  • is_diff_Rmult -> is_diff_mulr
• in measure.v:
  • measurable_fun_id -> measurable_id
  • measurable_fun_cst -> measurable_cst
  • measurable_fun_comp -> measurable_comp
  • measurable_funT_comp -> measurableT_comp
  • measurable_fun_fst -> measurable_fst
  • measurable_fun_snd -> measurable_snd
  • measurable_fun_swap -> measurable_swap
  • measurable_fun_pair -> measurable_fun_prod
  • isMeasure0 -> ``Content_isMeasure`
  • Hahn_ext -> measure_extension
  • Hahn_ext_ge0 -> measure_extension_ge0
  • Hahn_ext_sigma_additive -> measure_extension_semi_sigma_additive
  • Hahn_ext_unique -> measure_extension_unique
  • RingOfSets_from_semiRingOfSets -> SemiRingOfSets_isRingOfSets
  • AlgebraOfSets_from_RingOfSets -> RingOfSets_isAlgebraOfSets
  • Measurable_from_algebraOfSets -> AlgebraOfSets_isMeasurable
  • ring_sigma_additive -> ring_semi_sigma_additive
• in lebesgue_measure.v
  • measurable_funN -> measurable_oppr
  • emeasurable_fun_minus -> measurable_oppe
  • measurable_fun_abse -> measurable_abse
  • measurable_EFin -> measurable_image_EFin
  • measurable_fun_EFin -> measurable_EFin
  • measurable_fine -> measurable_image_fine
  • measurable_fun_fine -> measurable_fine
  • measurable_fun_normr -> measurable_normr
  • measurable_fun_exprn -> measurable_exprn
  • emeasurable_fun_max -> measurable_maxe
  • emeasurable_fun_min -> measurable_mine
  • measurable_fun_max -> measurable_maxr
  • measurable_fun_er_map -> measurable_er_map
  • emeasurable_fun_funepos -> measurable_funepos
  • emeasurable_fun_funeneg -> measurable_funeneg
  • measurable_funrM -> measurable_mulrl
• in lebesgue_integral.v:
  • measurable_fun_indic -> measurable_indic

Deprecated

• in lebesgue_measure.v:
  • lemma measurable_fun_sqr (use measurable_exprn instead)
  • lemma measurable_fun_opp (use measurable_oppr instead)

Removed

• in normedtype.v:
  • instance Proper_dnbhs_realType
• in measure.v:
  • instances ae_filter_algebraOfSetsType, ae_filter_measurableType, ae_properfilter_measurableType
• in lebesgue_measure.v:
  • lemma emeasurable_funN (use measurableT_comp) instead
  • lemma measurable_fun_prod1 (use measurableT_comp instead)
  • lemma measurable_fun_prod2 (use measurableT_comp instead)
• in lebesgue_integral.v
  • lemma emeasurable_funN (was already in lebesgue_measure.v, use measurableT_comp instead)

[0.6.2] - 2023-04-21

Added

• in mathcomp_extra.v:
  • lemma ler_sqrt
  • lemma lt_min_lt
• in classical_sets.v:
  • lemmas ltn_trivIset, subsetC_trivIset
• in contructive_ereal.v:
  • lemmas ereal_blatticeMixin, ereal_tblatticeMixin
  • canonicals ereal_blatticeType, ereal_tblatticeType
  • lemmas EFin_min, EFin_max
  • definition sqrte
  • lemmas sqrte0, sqrte_ge0, lee_sqrt, sqrteM, sqr_sqrte, sqrte_sqr, sqrte_fin_num
• in ereal.v:
  • lemmas compreBr, compre_scale
  • lemma le_er_map
• in set_interval.v:
  • lemma onem_factor
  • lemmas in1_subset_itv, subset_itvW
• in topology.v,
  • definitions totally_disconnected, and zero_dimensional.
  • lemmas component_closed, zero_dimension_prod, discrete_zero_dimension, zero_dimension_totally_disconnected, totally_disconnected_cvg, and totally_disconnected_prod.
  • definitions split_sym, gauge, gauge_uniformType_mixin, gauge_topologicalTypeMixin, gauge_filtered, gauge_topologicalType, gauge_uniformType, gauge_pseudoMetric_mixin, and gauge_pseudoMetricType.
  • lemmas iter_split_ent, gauge_ent, gauge_filter, gauge_refl, gauge_inv, gauge_split, gauge_countable_uniformity, and uniform_pseudometric_sup.
  • definitions discrete_ent, discrete_uniformType, discrete_ball, discrete_pseudoMetricType, and pseudoMetric_bool.
  • lemmas finite_compact, discrete_ball_center, compact_cauchy_cvg
• in normedtype.v:
  • lemmas cvg_at_right_filter, cvg_at_left_filter, cvg_at_right_within, cvg_at_left_within
• in sequences.v:
  • lemma seqDUIE
• in derive.v:
  • lemma derivable_within_continuous
• in realfun.v:
  • definition derivable_oo_continuous_bnd, lemma derivable_oo_continuous_bnd_within
• in exp.v:
  • lemma ln_power_pos
  • definition powere_pos, notation _ `^ _ in ereal_scope
  • lemmas powere_pos_EFin, powere_posyr, powere_pose0, powere_pose1, powere_posNyr powere_pos0r, powere_pos1r, powere_posNyr, fine_powere_pos, powere_pos_ge0, powere_pos_gt0, powere_pos_eq0, powere_posM, powere12_sqrt
  • lemmas derive_expR, convex_expR
  • lemmas power_pos_ge0, power_pos0, power_pos_eq0, power_posM, power_posAC, power12_sqrt, power_pos_inv1, power_pos_inv, power_pos_intmul
• in measure.v:
  • lemmas negligibleU, negligibleS
  • definition almost_everywhere_notation
  • instances ae_filter_ringOfSetsType, ae_filter_algebraOfSetsType, ae_filter_measurableType
  • instances ae_properfilter_algebraOfSetsType, ae_properfilter_measurableType
• in lebesgue_measure.v:
  • lemma emeasurable_itv
  • lemma measurable_fun_er_map
  • lemmas measurable_fun_ln, measurable_fun_power_pos
• in lebesgue_integral.v:
  • lemma sfinite_Fubini
  • instance of isMeasurableFun for normr
  • lemma finite_measure_integrable_cst
  • lemma ae_ge0_le_integral
  • lemma ae_eq_refl
• new file convex.v:
  • mixin isConvexSpace, structure ConvexSpace, notations convType, _ <| _ |> _
  • lemmas conv1, second_derivative_convex
• new file charge.v:
  • mixin isAdditiveCharge, structure AdditiveCharge, notations additive_charge, {additive_charge set T -> \bar R}
  • mixin isCharge, structure Charge, notations charge, {charge set T -> \bar R}
  • lemmas charge0, charge_semi_additiveW, charge_semi_additive2E, charge_semi_additive2, chargeU, chargeDI, chargeD, charge_partition
  • definitions crestr, cszero, cscale, positive_set, negative_set
  • lemmas negative_set_charge_le0, negative_set0, bigcup_negative_set, negative_setU, positive_negative0
  • definition hahn_decomposition
  • lemmas hahn_decomposition_lemma, Hahn_decomposition, Hahn_decomposition_uniq
• new file itv.v:
  • definition wider_itv
  • module Itv:
    • definitions map_itv_bound, map_itv
    • lemmas le_map_itv_bound, subitv_map_itv
    • definition itv_cond
    • record def
    • notation spec
    • record typ
    • definitions mk, from, fromP
  • notations {itv R & i}, {i01 R}, %:itv, [itv of _], inum, %:inum
  • definitions itv_eqMixin, itv_choiceMixin, itv_porderMixin
  • canonical itv_subType, itv_eqType, itv_choiceType, itv_porderType
  • lemma itv_top_typ_subproof
  • canonical itv_top_typ
  • lemma typ_inum_subproof
  • canonical typ_inum
  • notation unify_itv
  • lemma itv_intro
  • definition empty_itv
  • lemmas itv_bottom, itv_gt0, itv_le0F, itv_lt0, itv_ge0F, itv_ge0, lt0F, le0, gt0F, lt1, ge1F, le1, gt1F
  • lemma widen_itv_subproof
  • definition widen_itv
  • lemma widen_itvE
  • notation %:i01
  • lemma zero_inum_subproof
  • canonical zero_inum
  • lemma one_inum_subproof
  • canonical one_inum
  • definition opp_itv_bound_subdef
  • lemmas opp_itv_ge0_subproof, opp_itv_gt0_subproof, opp_itv_boundr_subproof, opp_itv_le0_subproof, opp_itv_lt0_subproof, opp_itv_boundl_subproof
  • definition opp_itv_subdef
  • lemma opp_inum_subproof
  • canonical opp_inum
  • definitions add_itv_boundl_subdef, add_itv_boundr_subdef, add_itv_subdef
  • lemma add_inum_subproof
  • canonical add_inum
  • definitions itv_bound_signl, itv_bound_signr, interval_sign
  • variant interval_sign_spec
  • lemma interval_signP
  • definitions mul_itv_boundl_subdef, mul_itv_boundr_subdef
  • lemmas mul_itv_boundl_subproof, mul_itv_boundrC_subproof, mul_itv_boundr_subproof, mul_itv_boundr'_subproof
  • definition mul_itv_subdef
  • lemmas map_itv_bound_min, map_itv_bound_max, mul_inum_subproof
  • canonical mul_inum
  • lemmas inum_eq, inum_le, inum_lt
• new file probability.v:
  • definition random_variable, notation {RV _ >-> _}
  • lemmas notin_range_measure, probability_range
  • definition distribution, instance of isProbability
  • lemma probability_distribution, integral_distribution
  • definition expectation, notation 'E_P[X]
  • lemmas expectation_cst, expectation_indic, integrable_expectation, expectationM, expectation_ge0, expectation_le, expectationD, expectationB
  • definition variance, 'V_P[X]
  • lemma varianceE
  • lemmas variance_ge0, variance_cst
  • lemmas markov, chebyshev,
  • mixin MeasurableFun_isDiscrete, structure discreteMeasurableFun, notation {dmfun aT >-> T}
  • definition discrete_random_variable, notation {dRV _ >-> _}
  • definitions dRV_dom_enum, dRV_dom, dRV_enum, enum_prob
  • lemmas distribution_dRV_enum, distribution_dRV, sum_enum_prob, dRV_expectation
  • definion pmf, lemma expectation_pmf

Changed

• in mathcomp_extra.v
  • lemmas eq_bigmax, eq_bigmin changed to respect P in the returned type.
• in constructive_ereal.v:
  • maxEFin changed to fine_max
  • minEFin changed to fine_min
• in exp.v:
  • generalize exp_fun and rename to power_pos
  • exp_fun_gt0 has now a condition and is renamed to power_pos_gt0
  • remove condition of exp_funr0 and rename to power_posr0
  • weaken condition of exp_funr1 and rename to power_posr1
  • weaken condition of exp_fun_inv and rename to power_pos_inv
  • exp_fun1 -> power_pos1
  • rename ler_exp_fun to ler_power_pos
  • exp_funD -> power_posD
  • weaken condition of exp_fun_mulrn and rename to power_pos_mulrn
  • the notation `^ has now scope real_scope
  • weaken condition of riemannR_gt0 and dvg_riemannR
• in measure.v:
  • generalize negligible to semiRingOfSetsType
  • definition almost_everywhere

Renamed

• in functions.v:
  • IsFun -> isFun
• in set_interval.v:
  • conv -> line_path
  • conv_id -> line_path_id
  • ndconv -> ndline_path
  • convEl -> line_pathEl
  • convEr -> line_pathEr
  • conv10 -> line_path10
  • conv0 -> line_path0
  • conv1 -> line_path1
  • conv_sym -> line_path_sym
  • conv_flat -> line_path_flat
  • leW_conv -> leW_line_path
  • ndconvE -> ndline_pathE
  • convK -> line_pathK
  • conv_inj -> line_path_inj
  • conv_bij -> line_path_bij
  • le_conv -> le_line_path
  • lt_conv -> lt_line_path
  • conv_itv_bij -> line_path_itv_bij
  • mem_conv_itv -> mem_line_path_itv
  • mem_conv_itvcc -> mem_line_path_itvcc
  • range_conv -> range_line_path
• in topology.v:
  • Topological.ax1 -> Topological.nbhs_pfilter
  • Topological.ax2 -> Topological.nbhsE
  • Topological.ax3 -> Topological.openE
  • entourage_filter -> entourage_pfilter
  • Uniform.ax1 -> Uniform.entourage_filter
  • Uniform.ax2 -> Uniform.entourage_refl
  • Uniform.ax3 -> Uniform.entourage_inv
  • Uniform.ax4 -> Uniform.entourage_split_ex
  • Uniform.ax5 -> Uniform.nbhsE
  • PseudoMetric.ax1 -> PseudoMetric.ball_center
  • PseudoMetric.ax2 -> PseudoMetric.ball_sym
  • PseudoMetric.ax3 -> PseudoMetric.ball_triangle
  • PseudoMetric.ax4 -> PseudoMetric.entourageE
• in measure.v:
  • emeasurable_fun_bool -> measurable_fun_bool
• in lebesgue_measure.v:
  • punct_eitv_bnd_pinfty -> punct_eitv_bndy
  • punct_eitv_ninfty_bnd -> punct_eitv_Nybnd
  • eset1_pinfty -> eset1y
  • eset1_ninfty -> eset1Ny
  • ErealGenOInfty.measurable_set1_ninfty -> ErealGenOInfty.measurable_set1Ny
  • ErealGenOInfty.measurable_set1_pinfty -> ErealGenOInfty.measurable_set1y
  • ErealGenCInfty.measurable_set1_ninfty -> ErealGenCInfty.measurable_set1Ny
  • ErealGenCInfty.measurable_set1_pinfty -> ErealGenCInfty.measurable_set1y

Deprecated

• in realsum.v:
  • psumB, interchange_sup, interchange_psum
• in distr.v:
  • dlet_lim, dlim_let, exp_split, exp_dlet, dlet_dlet, dmargin_dlet, dlet_dmargin, dfst_dswap, dsnd_dswap, dsndE, pr_dlet, exp_split, exp_dlet
• in measure.v:
  • lemma measurable_fun_ext
• in lebesgue_measure.v:
  • lemmas emeasurable_itv_bnd_pinfty, emeasurable_itv_ninfty_bnd (use emeasurable_itv instead)

Removed

• in lebesgue_integral.v:
  • lemma ae_eq_mul

[0.6.1] - 2023-02-24

Added

• in mathcomp_extra.v:
  • lemma add_onemK
  • function swap
• in file boolp.v,
  • new lemma forallp_asboolPn2.
• in classical_sets.v:
  • canonical unit_pointedType
  • lemmas setT0, set_unit, set_bool
  • lemmas xsection_preimage_snd, ysection_preimage_fst
  • lemma trivIset_mkcond
  • lemmas xsectionI, ysectionI
  • lemma coverE
  • new lemma preimage_range.
• in constructive_ereal.v:
  • lemmas EFin_sum_fine, sumeN
  • lemmas adde_defDr, adde_def_sum, fin_num_sumeN
  • lemma fin_num_adde_defr, adde_defN
  • lemma oppe_inj
  • lemmas expeS, fin_numX
  • lemmas adde_def_doppeD, adde_def_doppeB
  • lemma fin_num_sume_distrr
• in functions.v:
  • lemma countable_bijP
  • lemma patchE
• in numfun.v:
  • lemmas xsection_indic, ysection_indic
• in file topology.v,
  • definition perfect_set.
  • lemmas perfectTP, perfect_prod, and perfect_diagonal.
  • definitions countable_uniformity, countable_uniformityT, sup_pseudoMetric_mixin, sup_pseudoMetricType, and product_pseudoMetricType.
  • lemmas countable_uniformityP, countable_sup_ent, and countable_uniformity_metric.
  • definitions quotient_topology, and quotient_open.
  • lemmas pi_continuous, quotient_continuous, and repr_comp_continuous.
  • definitions hausdorff_accessible, separate_points_from_closed, and join_product.
  • lemmas weak_sep_cvg, weak_sep_nbhsE, weak_sep_openE, join_product_continuous, join_product_open, join_product_inj, and join_product_weak.
  • definition clopen.
  • lemmas clopenI, clopenU, clopenC, clopen0, clopenT, clopen_comp, connected_closure, clopen_separatedP, and clopen_connectedP.
  • new lemmas powerset_filter_fromP and compact_cluster_set1.
• in exp.v:
  • lemma expR_ge0
• in measure.v:
  • mixin isProbability, structure Probability, type probability
  • lemma probability_le1
  • definition discrete_measurable_unit
  • structures sigma_finite_additive_measure and sigma_finite_measure
  • lemmas measurable_curry, measurable_fun_fst, measurable_fun_snd, measurable_fun_swap, measurable_fun_pair, measurable_fun_if_pair
  • lemmas dirac0, diracT
  • lemma fin_num_fun_sigma_finite
  • structure FiniteMeasure, notation {finite_measure set _ -> \bar _}
  • definition sfinite_measure_def
  • mixin Measure_isSFinite_subdef, structure SFiniteMeasure, notation {sfinite_measure set _ -> \bar _}
  • mixin SigmaFinite_isFinite with field fin_num_measure, structure FiniteMeasure, notation {finite_measure set _ -> \bar _}
  • lemmas sfinite_measure_sigma_finite, sfinite_mzero, sigma_finite_mzero
  • factory Measure_isFinite, Measure_isSFinite
  • defintion sfinite_measure_seq, lemma sfinite_measure_seqP
  • mixin FiniteMeasure_isSubProbability, structure SubProbability, notation subprobability
  • factory Measure_isSubProbability
  • factory FiniteMeasure_isSubProbability
  • factory Measure_isSigmaFinite
  • lemmas fin_num_fun_lty, lty_fin_num_fun
  • definition fin_num_fun
  • structure FinNumFun
• in lebesgue_measure.v:
  • lemma measurable_fun_opp
• in lebesgue_integral.v
  • lemmas integral0_eq, fubini_tonelli
  • product measures now take {measure _ -> _} arguments and their theory quantifies over a {sigma_finite_measure _ -> _}.
  • notations \x, \x^ for product_measure1 and product_measure2

Changed

• in fsbigop.v:
  • implicits of eq_fsbigr
• in file topology.v,
  • lemma compact_near_coveringP
• in functions.v:
  • notation mem_fun_
• move from lebesgue_integral.v to classical_sets.v
  • lemmas trivIset_preimage1, trivIset_preimage1_in
• move from lebesgue_integral.v to numfun.v
  • lemmas fimfunE, fimfunEord, factory FiniteDecomp
  • lemmas fimfun_mulr_closed
  • canonicals fimfun_mul, fimfun_ring, fimfun_ringType
  • defintion fimfun_ringMixin
  • lemmas fimfunM, fimfun1, fimfun_prod, fimfunX, indic_fimfun_subproof.
  • definitions indic_fimfun, scale_fimfun, fimfun_comRingMixin
  • canonical fimfun_comRingType
  • lemma max_fimfun_subproof
  • mixin IsNonNegFun, structure NonNegFun, notation {nnfun _ >-> _}
• in measure.v:
  • order of arguments of isContent, Content, measure0, isMeasure0, Measure, isSigmaFinite, SigmaFiniteContent, SigmaFiniteMeasure

Renamed

• in measurable.v:
  • measurable_fun_comp -> measurable_funT_comp
• in numfun.v:
  • IsNonNegFun -> isNonNegFun
• in lebesgue_integral.v:
  • IsMeasurableFunP -> isMeasurableFun
• in measure.v:
  • {additive_measure _ -> _} -> {content _ -> _}
  • isAdditiveMeasure -> isContent
  • AdditiveMeasure -> Content
  • additive_measure -> content
  • additive_measure_snum_subproof -> content_snum_subproof
  • additive_measure_snum -> content_snum
  • SigmaFiniteAdditiveMeasure -> SigmaFiniteContent
  • sigma_finite_additive_measure -> sigma_finite_content
  • {sigma_finite_additive_measure _ -> _} -> {sigma_finite_content _ -> _}
• in constructive_ereal.v:
  • fin_num_adde_def -> fin_num_adde_defl
  • oppeD -> fin_num_oppeD
  • oppeB -> fin_num_oppeB
  • doppeD -> fin_num_doppeD
  • doppeB -> fin_num_doppeB
• in topology.v:
  • finSubCover -> finite_subset_cover
• in sequences.v:
  • eq_eseries -> eq_eseriesr
• in esum.v:
  • summable_nneseries_esum -> summable_eseries_esum
  • summable_nneseries -> summable_eseries

Generalized

• in classical_sets.v:
  • xsection_preimage_snd, ysection_preimage_fst
• in constructive_ereal.v:
  • oppeD, oppeB
• in esum.v:
  • lemma esum_esum
• in measure.v
  • lemma measurable_fun_comp
  • lemma measure_bigcup generalized,
  • lemma eq_measure
  • sigma_finite generalized from numFieldType to numDomainType
  • fin_num_fun_sigma_finite generalized from measurableType to algebraOfSetsType
• in lebesgue_integral.v:
  • lemma measurable_sfunP
  • lemma integrable_abse

Removed

• in esum.v:
  • lemma fsbig_esum

[0.6.0] - 2022-12-14

Added

• OPAM package coq-mathcomp-classical containing boolp.v
• file all_classical.v
• file classical/set_interval.v
• in mathcomp_extra.v
  • lemma lez_abs2n
  • lemmas pred_oappE and pred_oapp_set (from classical_sets.v)
  • lemma sumr_le0
  • new definition inv_fun.
  • new lemmas ler_ltP, and real_ltr_distlC.
  • new definitions proj, and dfwith.
  • new lemmas dfwithin, dfwithout, and dfwithP.
  • new lemma projK
  • generalize lemmas bigmax_le, bigmax_lt, lt_bigmin and le_bigmin from finType to Type
  • new definition oAC to turn an AC operator T -> T -> T, into a monoid com_law option T -> option T -> option T.
  • new generic lemmas opACE, some_big_AC, big_ACE, big_undup_AC, perm_big_AC, sub_big, sub_big_seq, sub_big_seq_cond, uniq_sub_big, uniq_sub_big_cond, sub_big_idem, sub_big_idem_cond, sub_in_big, le_big_ord, subset_big, subset_big_cond, le_big_nat_cond, le_big_nat, and le_big_ord_cond,
  • specialization to bigmax: sub_bigmax, sub_bigmax_seq, sub_bigmax_cond, sub_in_bigmax, le_bigmax_nat, le_bigmax_nat_cond, le_bigmax_ord, le_bigmax_ord_cond, subset_bigmax, and subset_bigmax_cond.
  • specialization to bigmin, sub_bigmax, sub_bigmin_seq, sub_bigmin_cond, sub_in_bigmin, le_bigmin_nat, le_bigmin_nat_cond, le_bigmin_ord, le_bigmin_ord_cond, subset_bigmin, and subset_bigmin_cond.
• in classical_sets.v
  • lemmas IIDn, IISl
  • lemmas set_compose_subset, compose_diag
  • notation \; for the composition of relations
  • notations \bigcup_(i < n) F and \bigcap_(i < n) F
  • new lemmas eq_image_id, subKimage, subimageK, and eq_imageK.
  • lemma bigsetU_sup
  • lemma image2_subset
• in constructive_ereal.v
  • lemmas fine_le, fine_lt, fine_abse, abse_fin_num
  • lemmas gte_addl, gte_addr
  • lemmas gte_daddl, gte_daddr
  • lemma lte_spadder, lte_spaddre
  • lemma lte_spdadder
  • lemma sum_fine
  • lemmas lteN10, leeN10
  • lemmas le0_fin_numE
  • lemmas fine_lt0, fine_le0
  • lemma fine_lt0E
  • multi-rules lteey, lteNye
  • new lemmas real_ltry, real_ltNyr, real_leey, real_leNye, fin_real, addNye, addeNy, gt0_muley, lt0_muley, gt0_muleNy, and lt0_muleNy.
  • new lemmas daddNye, and daddeNy.
  • lemma lt0e
  • canonicals maxe_monoid, maxe_comoid, mine_monoid, mine_comoid
• in functions.v,
  • new lemmas inv_oppr, preimageEoinv, preimageEinv, and inv_funK.
• in cardinality.v
  • lemmas eq_card1, card_set1, card_eqSP, countable_n_subset, countable_finite_subset, eq_card_fset_subset, fset_subset_countable
• in fsbigop.v:
  • lemmas fsumr_ge0, fsumr_le0, fsumr_gt0, fsumr_lt0, pfsumr_eq0, pair_fsbig, exchange_fsbig
  • lemma fsbig_setU_set1
• in ereal.v:
  • notation \sum_(_ \in _) _ (from fsbigop.v)
  • lemmas fsume_ge0, fsume_le0, fsume_gt0, fsume_lt0, pfsume_eq0, lee_fsum_nneg_subset, lee_fsum, ge0_mule_fsumr, ge0_mule_fsuml (from fsbigop.v)
  • lemmas finite_supportNe, dual_fsumeE, dfsume_ge0, dfsume_le0, dfsume_gt0, dfsume_lt0, pdfsume_eq0, le0_mule_dfsumr, le0_mule_dfsuml
  • lemma fsumEFin
  • new lemmas ereal_nbhs_pinfty_gt, ereal_nbhs_ninfty_lt, ereal_nbhs_pinfty_real, and ereal_nbhs_ninfty_real.
• in classical/set_interval.v:
  • definitions neitv, set_itv_infty_set0, set_itvE, disjoint_itv, conv, factor, ndconv (from set_interval.v)
  • lemmas neitv_lt_bnd, set_itvP, subset_itvP, set_itvoo, set_itv_cc, set_itvco, set_itvoc, set_itv1, set_itvoo0, set_itvoc0, set_itvco0, set_itv_infty_infty, set_itv_o_infty, set_itv_c_infty, set_itv_infty_o, set_itv_infty_c, set_itv_pinfty_bnd, set_itv_bnd_ninfty, setUitv1, setU1itv, set_itvI, neitvE, neitvP, setitv0, has_lbound_itv, has_ubound_itv, hasNlbound, hasNubound, opp_itv_bnd_infty, opp_itv_infty_bnd, opp_itv_bnd_bnd, opp_itvoo, setCitvl, setCitvr, set_itv_splitI, setCitv, set_itv_splitD, mem_1B_itvcc, conv_id, convEl, convEr, conv10, conv0, conv1, conv_sym, conv_flat, leW_conv, leW_factor, factor_flat, factorl, ndconvE, factorr, factorK, convK, conv_inj, factor_inj, conv_bij, factor_bij, le_conv, le_factor, lt_conv, lt_factor, conv_itv_bij, factor_itv_bij, mem_conv_itv, mem_conv_itvcc, range_conv, range_factor, mem_factor_itv, set_itv_ge, trivIset_set_itv_nth, disjoint_itvxx, lt_disjoint, disjoint_neitv, neitv_bnd1, neitv_bnd2 (from set_interval.v)
  • lemmas setNK, lb_ubN, ub_lbN, mem_NE, nonemptyN, opp_set_eq0, has_lb_ubN, has_ubPn, has_lbPn (from reals.v)
• in topology.v:
  • lemmas continuous_subspaceT, subspaceT_continuous
  • lemma weak_subspace_open
  • lemma weak_ent_filter, weak_ent_refl, weak_ent_inv, weak_ent_split, weak_ent_nbhs
  • definition map_pair, weak_ent, weak_uniform_mixin, weak_uniformType
  • lemma sup_ent_filter, sup_ent_refl, sup_ent_inv, sup_ent_split, sup_ent_nbhs
  • definition sup_ent, sup_uniform_mixin, sup_uniformType
  • definition product_uniformType
  • lemma uniform_entourage
  • definition weak_ball, weak_pseudoMetricType
  • lemma weak_ballE
  • lemma finI_from_countable
  • lemmas entourage_invI, split_ent_subset
  • definition countable_uniform_pseudoMetricType_mixin
  • lemmas closed_bigsetU, accessible_finite_set_closed
  • new lemmas eq_cvg, eq_is_cvg, eq_near, cvg_toP, cvgNpoint, filter_imply, nbhs_filter, near_fun, cvgnyPgt, cvgnyPgty, cvgnyPgey, fcvg_ballP, fcvg_ball, and fcvg_ball2P.
  • new lemmas dfwith_continuous, and proj_open.
• in topology.v, added near do and near=> x do tactic notations to perform some tactics under a \forall x \near F, ... quantification.
• in reals.v:
  • lemma floor0
• in normedtype.v,
  • lemmas closed_ballR_compact and locally_compactR
  • new lemmas nbhsNimage, nbhs_pinfty_real, nbhs_ninfty_real, pinfty_ex_ge, cvgryPger, cvgryPgtr, cvgrNyPler, cvgrNyPltr, cvgry_ger, cvgry_gtr, cvgrNy_ler, cvgrNy_ltr, cvgNry, cvgNrNy, cvgry_ge, cvgry_gt, cvgrNy_le, cvgrNy_lt, cvgeyPger, cvgeyPgtr, cvgeyPgty, cvgeyPgey, cvgeNyPler, cvgeNyPltr, cvgeNyPltNy, cvgeNyPleNy, cvgey_ger, cvgey_gtr, cvgeNy_ler, cvgeNy_ltr, cvgNey, cvgNeNy, cvgerNyP, cvgeyPge, cvgeyPgt, cvgeNyPle, cvgeNyPlt, cvgey_ge, cvgey_gt, cvgeNy_le, cvgeNy_lt, cvgenyP, normfZV, fcvgrPdist_lt, cvgrPdist_lt, cvgrPdistC_lt, cvgr_dist_lt, cvgr_distC_lt, cvgr_dist_le, cvgr_distC_le, nbhs_norm0P, cvgr0Pnorm_lt, cvgr0_norm_lt, cvgr0_norm_le, nbhsDl, nbhsDr, nbhs0P, nbhs_right0P, nbhs_left0P, nbhs_right_gt, nbhs_left_lt, nbhs_right_neq, nbhs_left_neq, nbhs_right_ge, nbhs_left_le, nbhs_right_lt, nbhs_right_le, nbhs_left_gt, nbhs_left_ge, nbhsr0P, cvgrPdist_le, cvgrPdist_ltp, cvgrPdist_lep, cvgrPdistC_le, cvgrPdistC_ltp, cvgrPdistC_lep, cvgr0Pnorm_le, cvgr0Pnorm_ltp, cvgr0Pnorm_lep, cvgr_norm_lt, cvgr_norm_le, cvgr_norm_gt, cvgr_norm_ge, cvgr_neq0, real_cvgr_lt, real_cvgr_le, real_cvgr_gt, real_cvgr_ge, cvgr_lt, cvgr_gt, cvgr_norm_lty, cvgr_norm_ley, cvgr_norm_gtNy, cvgr_norm_geNy, fcvgr2dist_ltP, cvgr2dist_ltP, cvgr2dist_lt, cvgNP, norm_cvg0P, cvgVP, is_cvgVE, cvgr_to_ge, cvgr_to_le, nbhs_EFin, nbhs_ereal_pinfty, nbhs_ereal_ninfty, fine_fcvg, fcvg_is_fine, fine_cvg, cvg_is_fine, cvg_EFin, neq0_fine_cvgP, cvgeNP, is_cvgeNE, cvge_to_ge, cvge_to_le, is_cvgeM, limeM, cvge_ge, cvge_le, lim_nnesum, ltr0_cvgV0, cvgrVNy, ler_cvg_to, gee_cvgy, lee_cvgNy, squeeze_fin, and lee_cvg_to.
• in normedtype.v, added notations ^'+, ^'-, +oo_R, -oo_R
• in sequences.v,
  • lemma invr_cvg0 and invr_cvg_pinfty
  • lemma cvgPninfty_lt, cvgPpinfty_near, cvgPninfty_near, cvgPpinfty_lt_near and cvgPninfty_lt_near
  • new lemma nneseries_pinfty.
  • lemmas is_cvg_ereal_npos_natsum_cond, lee_npeseries, is_cvg_npeseries_cond, is_cvg_npeseries, npeseries_le0, is_cvg_ereal_npos_natsum
  • lemma nnseries_is_cvg
• in measure.v:
  • definition discrete_measurable_bool with an instance of measurable type
  • lemmas measurable_fun_if, measurable_fun_ifT
  • lemma measurable_fun_bool
• in lebesgue_measure.v:
  • definition ErealGenInftyO.R and lemma ErealGenInftyO.measurableE
  • lemma sub1set
• in lebesgue_integral.v:
  • lemma integral_cstNy
  • lemma ae_eq0
  • lemma integral_cst
  • lemma le_integral_comp_abse
  • lemmas integral_fune_lt_pinfty, integral_fune_fin_num
  • lemmas emeasurable_fun_fsum, ge0_integral_fsum

Changed

• in constructive_ereal.v:
  • lemmas lee_paddl, lte_paddl, lee_paddr, lte_paddr, lte_spaddr, lee_pdaddl, lte_pdaddl, lee_pdaddr, lte_pdaddr, lte_spdaddr generalized to realDomainType
  • generalize lte_addl, lte_addr, gte_subl, gte_subr, lte_daddl, lte_daddr, gte_dsubl, gte_dsubr
• in topology.v
  • definition fct_restrictedUniformType changed to use weak_uniformType
  • definition family_cvg_topologicalType changed to use sup_uniformType
  • lemmas continuous_subspace0, continuous_subspace1
• in realfun.v:
  • Instance for GRing.opp over real intervals
  • lemmas itv_continuous_inj_le, itv_continuous_inj_ge, itv_continuous_inj_mono, segment_continuous_inj_le, segment_continuous_inj_ge, segment_can_le , segment_can_ge, segment_can_mono, segment_continuous_surjective, segment_continuous_le_surjective, segment_continuous_ge_surjective, continuous_inj_image_segment, continuous_inj_image_segmentP, segment_continuous_can_sym, segment_continuous_le_can_sym, segment_continuous_ge_can_sym, segment_inc_surj_continuous, segment_dec_surj_continuous, segment_mono_surj_continuous, segment_can_le_continuous, segment_can_ge_continuous, segment_can_continuous all have "{in I, continuous f}" replaced by "{within I, continuous f}"
• in sequence.v:
  • nneseries_pinfty generalized to eseries_pinfty
• in measure.v:
  • covered_by_countable generalized from pointedType to choiceType
• in lebesgue_measure.v:
  • definition fimfunE now uses fsbig
  • generalize and rename eitv_c_infty to eitv_bnd_infty and eitv_infty_c to eitv_infty_bnd
  • generalize ErealGenOInfty.G, ErealGenCInfty.G, ErealGenInftyO.G
• in lebesgue_integral.v:
  • implicits of ae_eq_integral
• moved from mathcomp_extra.v to classical_sets.v: pred_oappE, and pred_oapp_set.
• moved from normedtype.v to mathcomp_extra.v: itvxx, itvxxP, subset_itv_oo_cc, and bound_side.
• moved from sequences.v to normedtype.v: ler_lim.
• sub_dominatedl and sub_dominatedr generalized from numFieldType to numDomainType.
• abse_fin_num changed from an equivalence to an equality.
• lee_opp2 and lte_opp2 generalized from realDomainType to numDomainType.
• cvgN, cvg_norm, is_cvg_norm generalized from normedModType/topologicalType to pseudoMetricNormedZmodType/Type
• cvgV, is_cvgV, cvgM, is_cvgM, is_cvgMr, is_cvgMl, is_cvgMrE, is_cvgMlE, limV, cvg_abse, is_cvg_abse generalized from TopologicalType to Type
• lim_norm generalized from normedModType/TopoligicalType to pseudoMetricNormedZmodType/Type
• updated cvg_ballP, cvg_ball2P, cvg_ball, and cvgi_ballP to match a f @ F instead of just an F. The old lemmas are still available with prefix f.
• generalized lee_lim to any proper filter and moved from sequences.v to normedtype.v.
• generalized ereal_nbhs_pinfty_ge and ereal_nbhs_ninfty_le.
• renamed nbhsN to nbhsNimage and nbhsN is now replaced by nbhs (- x) = -%R @ x
• fixed the statements of nbhs_normP which used to be an accidental alias of nbhs_ballP together with nbhs_normE, nbhs_le_nbhs_norm, nbhs_norm_le_nbhs, near_nbhs_norm and nbhs_norm_ball which were not about nbhs_ball_ ball_norm but should have been.
• EFin_lim generalized from realType to realFieldType

Renamed

• file theories/mathcomp_extra.v moved to classical/mathcomp_extra.v
• file theories/boolp.v -> classical/boolp.v
• file theories/classical_sets.v -> classical/classical_sets.v
• file theories/functions.v -> classical/functions.v
• file theories/cardinality.v -> classical/cardinality.v
• file theories/fsbigop.v -> classical/fsbigop.v
• file theories/set_interval.v -> theories/real_interval.v
• in mathcomp_extra.v:
  • homo_le_bigmax -> le_bigmax2
• in constructive_ereal.v:
  • lte_spdaddr -> lte_spdaddre
  • esum_ninftyP -> esum_eqNyP
  • esum_ninfty -> esum_eqNy
  • esum_pinftyP -> esum_eqyP
  • esum_pinfty -> esum_eqy
  • desum_pinftyP -> desum_eqyP
  • desum_pinfty -> desum_eqy
  • desum_ninftyP -> desum_eqNyP
  • desum_ninfty -> desum_eqNy
  • eq_pinftyP -> eqyP
  • ltey -> ltry
  • ltNye -> ltNyr
• in topology.v:
  • renamed continuous_subspaceT to continuous_in_subspaceT
  • pasting -> withinU_continuous
  • cvg_map_lim -> cvg_lim
  • cvgi_map_lim -> cvgi_lim
  • app_cvg_locally -> cvg_ball
  • prod_topo_apply_continuous -> proj_continuous
• in normedtype.v,
  • normmZ -> normrZ
  • norm_cvgi_map_lim -> norm_cvgi_lim
  • nbhs_image_ERFin -> nbhs_image_EFin
• moved from sequences.v to normedtype.v:
  • squeeze -> squeeze_cvgr
• in sequences.v:
  • nneseries0 -> eseries0
  • nneseries_pred0 -> eseries_pred0
  • eq_nneseries -> eq_eseries
  • nneseries_mkcond -> eseries_mkcond
  • seqDUE -> seqDU_seqD
  • elim_sup -> lim_esup
  • elim_inf -> lim_einf
  • elim_inf_shift -> lim_einf_shift
  • elim_sup_le_cvg -> lim_esup_le_cvg
  • elim_infN -> lim_einfN
  • elim_supN -> lim_esupN
  • elim_inf_sup -> lim_einf_sup
  • cvg_ninfty_elim_inf_sup -> cvgNy_lim_einf_sup
  • cvg_ninfty_einfs -> cvgNy_einfs
  • cvg_ninfty_esups -> cvgNy_esups
  • cvg_pinfty_einfs -> cvgy_einfs
  • cvg_pinfty_esups -> cvgy_esups
  • cvg_elim_inf_sup -> cvg_lim_einf_sup
  • is_cvg_elim_infE -> is_cvg_lim_einfE
  • is_cvg_elim_supE -> is_cvg_lim_esupE
• in measure.v,
  • caratheodory_lim_lee -> caratheodory_lime_le
• in lebesgue_measure.v,
  • measurable_fun_elim_sup -> measurable_fun_lim_esup
• moved from lebesgue_measure.v to real_interval.v:
  • itv_cpinfty_pinfty -> itv_cyy
  • itv_opinfty_pinfty -> itv_oyy
  • itv_cninfty_pinfty -> itv_cNyy
  • itv_oninfty_pinfty -> itv_oNyy
• in lebesgue_integral.v:
  • integral_cst_pinfty -> integral_csty
  • sintegral_cst -> sintegral_EFin_cst
  • integral_cst -> integral_cstr

Generalized

• in constructive_ereal.v,
  • daddooe -> daddye
  • daddeoo -> daddey
  • ltey, ltNye
• moved from normedtype.v to mathcomp_extra.v:
  • ler0_addgt0P -> ler_gtP
• in normedtype.v,
  • cvg_gt_ge -> cvgr_ge
  • cvg_lt_le -> cvgr_le
  • cvg_dist0 -> norm_cvg0
  • ereal_cvgN -> cvgeN
  • ereal_is_cvgN -> is_cvgeN
  • ereal_cvgrM -> cvgeMl
  • ereal_is_cvgrM -> is_cvgeMl
  • ereal_cvgMr -> cvgeMr
  • ereal_is_cvgMr -> is_cvgeMr
  • ereal_limrM -> limeMl
  • ereal_limMr -> limeMr
  • ereal_limN -> limeN
  • linear_continuous0 -> continuous_linear_bounded
  • linear_bounded0 -> bounded_linear_continuous
• moved from derive.v to normedtype.v:
  • le0r_cvg_map -> limr_ge
  • ler0_cvg_map -> limr_le
• moved from sequences.v to normedtype.v:
  • ereal_cvgM -> cvgeM
  • cvgPpinfty -> cvgryPge
  • cvgPninfty -> cvgrNyPle
  • ger_cvg_pinfty -> ger_cvgy
  • ler_cvg_ninfty -> ler_cvgNy
  • cvgPpinfty_lt -> cvgryPgt
  • cvgPninfty_lt -> cvgrNyPlt
  • cvgPpinfty_near -> cvgryPgey
  • cvgPninfty_near -> cvgrNyPleNy
  • cvgPpinfty_lt_near -> cvgryPgty
  • cvgPninfty_lt_near -> cvgrNyPltNy
  • invr_cvg0 -> gtr0_cvgV0
  • invr_cvg_pinfty -> cvgrVy
  • nat_dvg_real -> cvgrnyP
  • ereal_cvg_abs0 -> cvg_abse0P
  • ereal_lim_ge -> lime_ge
  • ereal_lim_le -> lime_le
  • dvg_ereal_cvg -> cvgeryP
  • ereal_cvg_real -> fine_cvgP
  • ereal_squeeze -> squeeze_cvge
  • ereal_cvgD -> cvgeD
  • ereal_cvgB -> cvgeB
  • ereal_is_cvgD -> is_cvgeD
  • ereal_cvg_sub0 -> cvge_sub0
  • ereal_limD -> limeD
  • ereal_lim_sum -> cvg_nnesum
• moved from sequences.v to topology.v:
  • nat_cvgPpinfty -> cvgnyPge
• in topology.v
  • prod_topo_apply -> proj
• in lebesgue_integral.v:
  • integral_sum -> integral_nneseries

Deprecated

• in constructive_ereal.v:
  • lemma lte_spaddr, renamed lte_spaddre
• in topology.v, deprecated
  • cvg_ballPpos (use a combination of cvg_ballP and posnumP),
  • cvg_dist (use cvgr_dist_lt or a variation instead)
• in normedtype.v, deprecated
  • cvg_distP (use cvgrPdist_lt or a variation instead),
  • cvg_dist (use cvg_dist_lt or a variation instead),
  • cvg_distW (use cvgrPdist_le or a variation instead),
  • cvg_bounded_real (use cvgr_norm_lty or a variation instead),
  • continuous_cvg_dist (simply use the fact that (x --> l) -> (x = l)),
  • cvg_dist2P (use cvgr2dist_ltP or a variant instead),
  • cvg_dist2 (use cvgr2dist_lt or a variant instead),
• in derive.v, deprecated
  • ler_cvg_map (subsumed by ler_lim),
• in sequences.v, deprecated
  • cvgNpinfty (use cvgNry instead),
  • cvgNninfty (use cvgNrNy instead),
  • ereal_cvg_ge0 (use cvge_ge instead),
  • ereal_cvgPpinfty (use cvgeyPge or a variant instead),
  • ereal_cvgPninfty (use cvgeNyPle or a variant instead),
  • ereal_cvgD_pinfty_fin (use cvgeD instead),
  • ereal_cvgD_ninfty_fin (use cvgeD instead),
  • ereal_cvgD_pinfty_pinfty (use cvgeD instead),
  • ereal_cvgD_ninfty_ninfty (use cvgeD instead),
  • ereal_cvgM_gt0_pinfty (use cvgeM instead),
  • ereal_cvgM_lt0_pinfty (use cvgeM instead),
  • ereal_cvgM_gt0_ninfty (use cvgeM instead),
  • ereal_cvgM_lt0_ninfty (use cvgeM instead),

Removed

• in classical_sets.v:
  • lemmas pred_oappE and pred_oapp_set (moved to mathcomp_extra.v)
• in fsbigop.v:
  • notation \sum_(_ \in _) _ (moved to ereal.v)
  • lemma lee_fsum_nneg_subset, lee_fsum, ge0_mule_fsumr, ge0_mule_fsuml, fsume_ge0, fsume_le0, fsume_gt0, fsume_lt0, pfsume_eq0 (moved to ereal.v)
  • lemma pair_fsum (subsumed by pair_fsbig)
  • lemma exchange_fsum (subsumed by exchange_fsbig)
• in reals.v:
  • lemmas setNK, lb_ubN, ub_lbN, mem_NE, nonemptyN, opp_set_eq0, has_lb_ubN, has_ubPn, has_lbPn (moved to classical/set_interval.v)
• in set_interval.v:
  • definitions neitv, set_itv_infty_set0, set_itvE, disjoint_itv, conv, factor, ndconv (moved to classical/set_interval.v)
  • lemmas neitv_lt_bnd, set_itvP, subset_itvP, set_itvoo, set_itv_cc, set_itvco, set_itvoc, set_itv1, set_itvoo0, set_itvoc0, set_itvco0, set_itv_infty_infty, set_itv_o_infty, set_itv_c_infty, set_itv_infty_o, set_itv_infty_c, set_itv_pinfty_bnd, set_itv_bnd_ninfty, setUitv1, setU1itv, set_itvI, neitvE, neitvP, setitv0, has_lbound_itv, has_ubound_itv, hasNlbound, hasNubound, opp_itv_bnd_infty, opp_itv_infty_bnd, opp_itv_bnd_bnd, opp_itvoo, setCitvl, setCitvr, set_itv_splitI, setCitv, set_itv_splitD, mem_1B_itvcc, conv_id, convEl, convEr, conv10, conv0, conv1, conv_sym, conv_flat, leW_conv, leW_factor, factor_flat, factorl, ndconvE, factorr, factorK, convK, conv_inj, factor_inj, conv_bij, factor_bij, le_conv, le_factor, lt_conv, lt_factor, conv_itv_bij, factor_itv_bij, mem_conv_itv, mem_conv_itvcc, range_conv, range_factor, mem_factor_itv, set_itv_ge, trivIset_set_itv_nth, disjoint_itvxx, lt_disjoint, disjoint_neitv, neitv_bnd1, neitv_bnd2 (moved to classical/set_interval.v)
• in topology.v
  • lemmas prod_topo_applyE

[0.5.4] - 2022-09-07

Added

• in mathcomp_extra.v:
  • defintion onem and notation `1-
  • lemmas onem0, onem1, onemK, onem_gt0, onem_ge0, onem_le1, onem_lt1, onemX_ge0, onemX_lt1, onemD, onemMr, onemM
  • lemmas natr1, nat1r
• in classical_sets.v:
  • lemmas subset_fst_set, subset_snd_set, fst_set_fst, snd_set_snd, fset_setM, snd_setM, fst_setMR
  • lemmas xsection_snd_set, ysection_fst_set
• in constructive_ereal.v:
  • lemmas ltNye_eq, sube_lt0, subre_lt0, suber_lt0, sube_ge0
  • lemmas dsubre_gt0, dsuber_gt0, dsube_gt0, dsube_le0
• in signed.v:
  • lemmas onem_PosNum, onemX_NngNum
• in fsbigop.v:
  • lemmas lee_fsum_nneg_subset, lee_fsum
• in topology.v:
  • lemma near_inftyS
  • lemma continuous_closedP, closedU, pasting
  • lemma continuous_inP
  • lemmas open_setIS, open_setSI, closed_setIS, closed_setSI
• in normedtype.v:
  • definitions contraction and is_contraction
  • lemma contraction_fixpoint_unique
• in sequences.v:
  • lemmas contraction_dist, contraction_cvg, contraction_cvg_fixed, banach_fixed_point, contraction_unique
• in derive.v:
  • lemma diff_derivable
• in measure.v:
  • lemma measurable_funTS
• in lebesgue_measure.v:
  • lemma measurable_fun_fine
  • lemma open_measurable_subspace
  • lemma subspace_continuous_measurable_fun
  • corollary open_continuous_measurable_fun
  • Hint about measurable_fun_normr
• in lebesgue_integral.v:
  • lemma measurable_fun_indic
  • lemma ge0_integral_mscale
  • lemma integral_pushforward

Changed

• in esum.v:
  • definition esum
• moved from lebesgue_integral.v to classical_sets.v:
  • mem_set_pair1 -> mem_xsection
  • mem_set_pair2 -> mem_ysection
• in derive.v:
  • generalized is_diff_scalel
• in measure.v:
  • generalize measurable_uncurry
• in lebesgue_measure.v:
  • pushforward requires a proof that its argument is measurable
• in lebesgue_integral.v:
  • change implicits of integralM_indic

Renamed

• in constructive_ereal.v:
  • lte_pinfty_eq -> ltey_eq
  • le0R -> fine_ge0
  • lt0R -> fine_gt0
• in ereal.v:
  • lee_pinfty_eq -> leye_eq
  • lee_ninfty_eq -> leeNy_eq
• in esum.v:
  • esum0 -> esum1
• in sequences.v:
  • nneseries_lim_ge0 -> nneseries_ge0
• in measure.v:
  • ring_fsets -> ring_finite_set
  • discrete_measurable -> discrete_measurable_nat
  • cvg_mu_inc -> nondecreasing_cvg_mu
• in lebesgue_integral.v:
  • muleindic_ge0 -> nnfun_muleindic_ge0
  • mulem_ge0 -> mulemu_ge0
  • nnfun_mulem_ge0 -> nnsfun_mulemu_ge0

Removed

• in esum.v:
  • lemma fsetsP, sum_fset_set

[0.5.3] - 2022-08-10

Added

• in mathcomp_extra.v:
  • lemma big_const_idem
  • lemma big_id_idem
  • lemma big_rem_AC
  • lemma bigD1_AC
  • lemma big_mkcond_idem
  • lemma big_split_idem
  • lemma big_id_idem_AC
  • lemma bigID_idem
  • lemmas bigmax_le and bigmax_lt
  • lemma bigmin_idr
  • lemma bigmax_idr
• in file boolp.v:
  • lemmas iter_compl, iter_compr, iter0
• in file functions.v:
  • lemmas oinv_iter, some_iter_inv, inv_iter,
  • Instances for functions interfaces for iter (partial inverse up to bijective function)
• in classical_sets.v:
  • lemma preimage10P
  • lemma setT_unit
  • lemma subset_refl
• in ereal.v:
  • notations _ < _ :> _ and _ <= _ :> _
  • lemmas lee01, lte01, lee0N1, lte0N1
  • lemmas lee_pmul2l, lee_pmul2r, lte_pmul, lee_wpmul2l
  • lemmas lee_lt_add, lee_lt_dadd, lee_paddl, lee_pdaddl, lte_paddl, lte_pdaddl, lee_paddr, lee_pdaddr, lte_paddr, lte_pdaddr
  • lemmas muleCA, muleAC, muleACA
• in reals.v:
  • lemmas Rfloor_lt_int, floor_lt_int, floor_ge_int
  • lemmas ceil_ge_int, ceil_lt_int
• in lebesgue_integral.v:
  • lemma ge0_emeasurable_fun_sum
  • lemma integrableMr

Changed

• in ereal.v:
  • generalize lee_pmul
  • simplify lte_le_add, lte_le_dadd, lte_le_sub, lte_le_dsub
• in measure.v:
  • generalize pushforward
• in lebesgue_integral.v
  • change Arguments of eq_integrable
  • fix pretty-printing of {mfun _ >-> _}, {sfun _ >-> _}, {nnfun _ >-> _}
  • minor generalization of eq_measure_integral
• from topology.v to mathcomp_extra.v:
  • generalize ltr_bigminr to porderType and rename to bigmin_lt
  • generalize bigminr_ler to orderType and rename to bigmin_le
• moved out of module Bigminr in normedtype.v to mathcomp_extra.v and generalized to orderType:
  • lemma bigminr_ler_cond, renamed to bigmin_le_cond
• moved out of module Bigminr in normedtype.v to mathcomp_extra.v:
  • lemma bigminr_maxr
• moved from from module Bigminr in normedtype.v
  • to mathcomp_extra.v and generalized to orderType
    • bigminr_mkcond -> bigmin_mkcond
    • bigminr_split -> bigmin_split
    • bigminr_idl -> bigmin_idl
    • bigminrID -> bigminID
    • bigminrD1 -> bigminD1
    • bigminr_inf -> bigmin_inf
    • bigminr_gerP -> bigmin_geP
    • bigminr_gtrP -> bigmin_gtP
    • bigminr_eq_arg -> bigmin_eq_arg
    • eq_bigminr -> eq_bigmin
  • to topology.v and generalized to orderType
    • bigminr_lerP -> bigmin_leP
    • bigminr_ltrP -> bigmin_ltP
• moved from topology.v to mathcomp_extra.v:
  • bigmax_lerP -> bigmax_leP
  • bigmax_ltrP -> bigmax_ltP
  • ler_bigmax_cond -> le_bigmax_cond
  • ler_bigmax -> le_bigmax
  • le_bigmax -> homo_le_bigmax

Renamed

• in ereal.v:
  • lee_pinfty_eq -> leye_eq
  • lee_ninfty_eq -> leeNy_eq
• in classical_sets.v:
  • set_bool -> setT_bool
• in topology.v:
  • bigmax_gerP -> bigmax_geP
  • bigmax_gtrP -> bigmax_gtP
• in lebesgue_integral.v:
  • emeasurable_funeM -> measurable_funeM

Removed

• in topology.v:
  • bigmax_seq1, bigmax_pred1_eq, bigmax_pred1
• in normedtype.v (module Bigminr)
  • bigminr_ler_cond, bigminr_ler.
  • bigminr_seq1, bigminr_pred1_eq, bigminr_pred1

Misc

• file ereal.v split in two files constructive_ereal.v and ereal.v (the latter exports the former, so the "Require Import ereal" can just be kept unchanged)

[0.5.2] - 2022-07-08

Added

• in file classical_sets.v
  • lemma set_bool
  • lemma supremum_out
  • definition isLub
  • lemma supremum1
  • lemma trivIset_set0
  • lemmas trivIset_image, trivIset_comp
  • notation trivIsets
• in file topology.v:
  • definition near_covering
  • lemma compact_near_coveringP
  • lemma continuous_localP, equicontinuous_subset_id
  • lemmas precompact_pointwise_precompact, precompact_equicontinuous, Ascoli
  • definition frechet_filter, instances frechet_properfilter, and frechet_properfilter_nat
  • definition principal_filter discrete_space
  • lemma principal_filterP, principal_filter_proper, principal_filter_ultra
  • canonical bool_discrete_filter
  • lemma compactU
  • lemma discrete_sing, discrete_nbhs, discrete_open, discrete_set1, discrete_closed, discrete_cvg, discrete_hausdorff
  • canonical bool_discrete_topology
  • definition discrete_topological_mixin
  • lemma discrete_bool, bool_compact
• in Rstruct.v:
  • lemmas Rsupremums_neq0, Rsup_isLub, Rsup_ub
• in reals.v:
  • lemma floor_natz
  • lemma opp_set_eq0, ubound0, lboundT
• in file lebesgue_integral.v:
  • lemma integrable0
  • mixins isAdditiveMeasure, isMeasure0, isMeasure, isOuterMeasure
  • structures AdditiveMeasure, Measure, OuterMeasure
  • notations additive_measure, measure, outer_measure
  • definition mrestr
  • lemmas integral_measure_sum_nnsfun, integral_measure_add_nnsfun
  • lemmas ge0_integral_measure_sum, integral_measure_add, integral_measure_series_nnsfun, ge0_integral_measure_series
  • lemmas integrable_neg_fin_num, integrable_pos_fin_num
  • lemma integral_measure_series
  • lemmas counting_dirac, summable_integral_dirac, integral_count
  • lemmas integrable_abse, integrable_summable, integral_bigcup
• in measure.v:
  • lemmas additive_measure_snum_subproof, measure_snum_subproof
  • canonicals additive_measure_snum, measure_snum
  • definition mscale
  • definition restr
  • definition counting, canonical measure_counting
  • definition discrete_measurable, instantiated as a measurableType
  • lemma sigma_finite_counting
  • lemma msum_mzero
• in lebesgue_measure.v:
  • lemma diracE
  • notation _.-ocitv
  • definition ocitv_display
• in file cardinality.v:
  • lemmas trivIset_sum_card, fset_set_sub, fset_set_set0
• in file sequences.v:
  • lemmas nat_dvg_real, nat_cvgPpinfty, nat_nondecreasing_is_cvg
  • definition nseries, lemmas le_nseries, cvg_nseries_near, dvg_nseries
• in file ereal.v:
  • lemma fin_num_abs
• in file esum.v:
  • definition summable
  • lemmas summable_pinfty, summableE, summableD, summableN, summableB, summable_funepos, summable_funeneg
  • lemmas summable_fine_sum, summable_cvg, summable_nneseries_lim, summable_nnseries, summable_nneseries_esum, esumB
  • lemma fsbig_esum
• in trigo.v:
  • lemmas cos1_gt0, pi_ge2
  • lemmas pihalf_ge1, pihalf_lt2
• in measure.v:
  • inductive measure_display
  • notation _.-sigma, _.-sigma.-measurable, _.-ring, _.-ring.-measurable, _.-cara, _.-cara.-measurable, _.-caratheodory, _.-prod. _.-prod.-measurable
  • notation _.-measurable
  • lemma measure_semi_additive_ord, measure_semi_additive_ord_I
  • lemma decomp_finite_set
• in functions.v:
  • lemma patch_pred, trivIset_restr
• has_sup1, has_inf1 moved from reals.v to classical_sets.v

Changed

• in topology.v:
  • generalize cluster_cvgE, fam_cvgE, ptws_cvg_compact_family
  • rewrite equicontinuous and pointwise_precompact to use index
• in Rstruct.v:
  • statement of lemma completeness', renamed to Rcondcomplete
  • statement of lemma real_sup_adherent
• in ereal.v:
  • statements of lemmas ub_ereal_sup_adherent, lb_ereal_inf_adherent
• in reals.v:
  • definition sup
  • statements of lemmas sup_adherent, inf_adherent
• in sequences.v:
  • generalize eq_nneseries, nneseries0
• in mathcomp_extra.v:
  • generalize card_fset_sum1
• in lebesgue_integral.v:
  • change the notation \int_
  • product_measure1 takes a proof that the second measure is sigma-finite
  • product_measure2 takes a proof that the first measure is sigma-finite
  • definitions integral and integrable now take a function instead of a measure
  • remove one space in notation \d_
  • generalize nondecreasing_series
  • constant measurableType now take an addititional parameter of type measure_display
• in measure.v:
  • measure0 is now a lemma
  • statement of lemmas content_fin_bigcup, measure_fin_bigcup, ring_fsets, decomp_triv, cover_decomp, decomp_set0, decompN0, Rmu_fin_bigcup
  • definitions decomp, measure
  • several constants now take a parameter of type measure_display
• in trigo.v:
  • lemma cos_exists
• in set_interval.v:
  • generalize to numDomainType:
    • mem_1B_itvcc, conv, conv_id, convEl, convEr, conv10, conv0, conv1, conv_sym, conv_flat, leW_conv, factor, leW_factor, factor_flat, factorl, ndconv, ndconvE
  • generalize to numFieldType
    • factorr, factorK, convK, conv_inj, factor_inj, conv_bij, factor_bij, le_conv, le_factor, lt_conv, lt_factor, conv_itv_bij, factor_itv_bij, mem_conv_itv, mem_conv_itvcc, range_conv, range_factor
  • generalize to realFieldType:
    • mem_factor_itv
• in fsbig.v:
  • generalize exchange_fsum
• lemma preimage_cst generalized and moved from lebesgue_integral.v to functions.v
• lemma fset_set_image moved from measure.v to cardinality.v
• in reals.v:
  • type generalization of has_supPn

Renamed

• in lebesgue_integral.v:
  • integralK -> integralrM
• in trigo.v:
  • cos_pihalf_uniq -> cos_02_uniq
• in measure.v:
  • sigma_algebraD -> sigma_algebraCD
  • g_measurable -> salgebraType
  • g_measurable_eqType -> salgebraType_eqType
  • g_measurable_choiceType -> salgebraType_choiceType
  • g_measurable_ptType -> salgebraType_ptType
• in lebesgue_measure.v:
  • itvs -> ocitv_type
  • measurable_fun_sum -> emeasurable_fun_sum
• in classical_sets.v:
  • trivIset_restr -> trivIset_widen
  • supremums_set1 -> supremums1
  • infimums_set1 -> infimums1

Removed

• in Rstruct.v:
  • definition real_sup
  • lemma real_sup_is_lub, real_sup_ub, real_sup_out
• in reals.v:
  • field sup from mixin_of in module Real
• in measure.v:
  • notations [additive_measure _ -> _], [measure _ -> _], [outer_measure _ -> _ ],
  • lemma measure_is_additive_measure
  • definitions caratheodory_measure_mixin, caratheodory_measure
  • coercions measure_to_nadditive_measure, measure_additive_measure
  • canonicals measure_additive_measure, set_ring_measure, outer_measure_of_measure, Hahn_ext_measure
  • lemma Rmu0
  • lemma measure_restrE
• in measure.v:
  • definition g_measurableType
  • notation mu.-measurable

[0.5.1] - 2022-06-04

Added

• in mathcomp_extra.v:
  • lemma card_fset_sum1
• in classical_sets.v:
  • lemma preimage_setT
  • lemma bigsetU_bigcup
  • lemmas setI_II and setU_II
• in topology.v:
  • definition powerset_filter_from
  • globals powerset_filter_from_filter
  • lemmas near_small_set, small_set_sub
  • lemmas withinET, closureEcvg, entourage_sym, fam_nbhs
  • generalize cluster_cvgE, ptws_cvg_compact_family
  • lemma near_compact_covering
  • rewrite equicontinuous and pointwise_precompact to use index
  • lemmas ptws_cvg_entourage, equicontinuous_closure, ptws_compact_cvg ptws_compact_closed, ascoli_forward, compact_equicontinuous
• in normedtype.v:
  • definition bigcup_ointsub
  • lemmas bigcup_ointsub0, open_bigcup_ointsub, is_interval_bigcup_ointsub, bigcup_ointsub_sub, open_bigcup_rat
  • lemmas mulrl_continuous and mulrr_continuous.
• in ereal.v:
  • definition expe with notation ^+
  • definition enatmul with notation *+ (scope %E)
  • definition ednatmul with notation *+ (scope %dE)
  • lemmas fineM, enatmul_pinfty, enatmul_ninfty, EFin_natmul, mule2n, expe2, mule_natl
  • lemmas ednatmul_pinfty, ednatmul_ninfty, EFin_dnatmul, dmule2n, ednatmulE, dmule_natl
  • lemmas sum_fin_num, sum_fin_numP
  • lemmas oppeB, doppeB, fineB, dfineB
  • lemma abse1
  • lemma ltninfty_adde_def
• in esum.v:
  • lemma esum_set1
  • lemma nnseries_interchange
• in cardinality.v:
  • lemma fset_set_image, card_fset_set, geq_card_fset_set, leq_card_fset_set, infinite_set_fset, infinite_set_fsetP and fcard_eq.
• in sequences.v:
  • lemmas nneseriesrM, ereal_series_cond, ereal_series, nneseries_split
  • lemmas lee_nneseries
• in numfun.v:
  • lemma restrict_lee
• in measure.v:
  • definition pushforward and canonical pushforward_measure
  • definition dirac with notation \d_ and canonical dirac_measure
  • lemmas finite_card_dirac, infinite_card_dirac
  • lemma eq_measure
  • definition msum and canonical measure_sum'
  • definition mzero and canonical measure_zero'
  • definition measure_add and lemma measure_addE
  • definition mseries and canonical measure_series'
• in set_interval.v:
  • lemma opp_itv_infty_bnd
• in lebesgue_integral.v:
  • lemmas integral_set0, ge0_integral_bigsetU, ge0_integral_bigcup
• in lebesgue_measure.v:
  • lemmas is_interval_measurable, open_measurable, continuous_measurable_fun
  • lemma emeasurable_funN
  • lemmas itv_bnd_open_bigcup, itv_bnd_infty_bigcup, itv_infty_bnd_bigcup, itv_open_bnd_bigcup
  • lemma lebesgue_measure_set1
  • lemma lebesgue_measure_itv
  • lemma lebesgue_measure_rat
• in lebesgue_integral.v:
  • lemmas integralM_indic, integralM_indic_nnsfun, integral_dirac
  • lemma integral_measure_zero
  • lemma eq_measure_integral

Changed

• in mathcomp_extra.v:
  • generalize card_fset_sum1
• in classical_sets.v:
  • lemma some_bigcup generalized and renamed to image_bigcup
• in esumv:
  • remove one hypothesis in lemmas reindex_esum, esum_image
• moved from lebesgue_integral.v to lebesgue_measure.v and generalized
  • hint measurable_set1/emeasurable_set1
• in sequences.v:
  • generalize eq_nneseries, nneseries0
• in set_interval.v:
  • generalize opp_itvoo to opp_itv_bnd_bnd
• in lebesgue_integral.v:
  • change the notation \int_

Renamed

• in ereal.v:
  • num_abs_le -> num_abse_le
  • num_abs_lt -> num_abse_lt
  • addooe -> addye
  • addeoo -> addey
  • mule_ninfty_pinfty -> mulNyy
  • mule_pinfty_ninfty -> mulyNy
  • mule_pinfty_pinfty -> mulyy
  • mule_ninfty_ninfty -> mulNyNy
  • lte_0_pinfty -> lt0y
  • lte_ninfty_0 -> ltNy0
  • lee_0_pinfty -> le0y
  • lee_ninfty_0 -> leNy0
  • lte_pinfty -> ltey
  • lte_ninfty -> ltNye
  • lee_pinfty -> leey
  • lee_ninfty -> leNye
  • mulrpinfty_real -> real_mulry
  • mulpinftyr_real -> real_mulyr
  • mulrninfty_real -> real_mulrNy
  • mulninftyr_real -> real_mulNyr
  • mulrpinfty -> mulry
  • mulpinftyr -> mulyr
  • mulrninfty -> mulrNy
  • mulninftyr -> mulNyr
  • gt0_mulpinfty -> gt0_mulye
  • lt0_mulpinfty -> lt0_mulye
  • gt0_mulninfty -> gt0_mulNye
  • lt0_mulninfty -> lt0_mulNye
  • maxe_pinftyl -> maxye
  • maxe_pinftyr -> maxey
  • maxe_ninftyl -> maxNye
  • maxe_ninftyr -> maxeNy
  • mine_ninftyl -> minNye
  • mine_ninftyr -> mineNy
  • mine_pinftyl -> minye
  • mine_pinftyr -> miney
  • mulrinfty_real -> real_mulr_infty
  • mulrinfty -> mulr_infty
• in realfun.v:
  • exp_continuous -> exprn_continuous
• in sequences.v:
  • ereal_pseriesD -> nneseriesD
  • ereal_pseries0 -> nneseries0
  • ereal_pseries_pred0 -> nneseries_pred0
  • eq_ereal_pseries -> eq_nneseries
  • ereal_pseries_sum_nat -> nneseries_sum_nat
  • ereal_pseries_sum -> nneseries_sum
  • ereal_pseries_mkcond -> nneseries_mkcond
  • ereal_nneg_series_lim_ge -> nneseries_lim_ge
  • is_cvg_ereal_nneg_series_cond -> is_cvg_nneseries_cond
  • is_cvg_ereal_nneg_series -> is_cvg_nneseries
  • ereal_nneg_series_lim_ge0 -> nneseries_lim_ge0
  • adde_def_nneg_series -> adde_def_nneseries
• in esum.v:
  • ereal_pseries_esum -> nneseries_esum
• in numfun.v:
  • funenng -> funepos
  • funennp -> funeneg
  • funenng_ge0 -> funepos_ge0
  • funennp_ge0 -> funeneg_ge0
  • funenngN -> funeposN
  • funennpN -> funenegN
  • funenng_restrict -> funepos_restrict
  • funennp_restrict -> funeneg_restrict
  • ge0_funenngE -> ge0_funeposE
  • ge0_funennpE -> ge0_funenegE
  • le0_funenngE -> le0_funeposE
  • le0_funennpE -> le0_funenegE
  • gt0_funenngM -> gt0_funeposM
  • gt0_funennpM -> gt0_funenegM
  • lt0_funenngM -> lt0_funeposM
  • lt0_funennpM -> lt0_funenegM
  • funenngnnp -> funeposneg
  • add_def_funennpg -> add_def_funeposneg
  • funeD_Dnng -> funeD_Dpos
  • funeD_nngD -> funeD_posD
• in lebesgue_measure.v:
  • emeasurable_fun_funenng -> emeasurable_fun_funepos
  • emeasurable_fun_funennp -> emeasurable_fun_funeneg
• in lebesgue_integral.v:
  • integrable_funenng -> integrable_funepos
  • integrable_funennp -> integrable_funeneg
  • integral_funennp_lt_pinfty -> integral_funeneg_lt_pinfty
  • integral_funenng_lt_pinfty -> integral_funepos_lt_pinfty
  • ae_eq_funenng_funennp -> ae_eq_funeposneg

Removed

• in mathcomp_extra.v:
  • lemmas natr_absz, ge_pinfty, le_ninfty, gt_pinfty, lt_ninfty
• in classical_sets.v:
  • notation [set of _]
• in topology.v:
  • lemmas inj_can_sym_in_on, inj_can_sym_on, inj_can_sym_in

[0.5.0] - 2022-03-23

Added

• in signed.v:
  • notations %:nngnum and %:posnum
• in ereal.v:
  • notations {posnum \bar R} and {nonneg \bar R}
  • notations %:pos and %:nng in ereal_dual_scope and ereal_scope
  • variants posnume_spec and nonnege_spec
  • definitions posnume, nonnege, abse_reality_subdef, ereal_sup_reality_subdef, ereal_inf_reality_subdef
  • lemmas ereal_comparable, pinfty_snum_subproof, ninfty_snum_subproof, EFin_snum_subproof, fine_snum_subproof, oppe_snum_subproof, adde_snum_subproof, dadde_snum_subproof, mule_snum_subproof, abse_reality_subdef, abse_snum_subproof, ereal_sup_snum_subproof, ereal_inf_snum_subproof, num_abse_eq0, num_lee_maxr, num_lee_maxl, num_lee_minr, num_lee_minl, num_lte_maxr, num_lte_maxl, num_lte_minr, num_lte_minl, num_abs_le, num_abs_lt, posnumeP, nonnegeP
  • signed instances pinfty_snum, ninfty_snum, EFin_snum, fine_snum, oppe_snum, adde_snum, dadde_snum, mule_snum, abse_snum, ereal_sup_snum, ereal_inf_snum

Changed

• in functions.v:
  • addrfunE renamed to addrfctE and generalized to Type, zmodType
  • opprfunE renamed to opprfctE and generalized to Type, zmodType
• moved from functions.v to classical_sets.v
  • lemma subsetW, definition subsetCW
• in mathcomp_extra.v:
  • fix notation ltLHS

Renamed

• in topology.v:
  • open_bigU -> bigcup_open
• in functions.v:
  • mulrfunE -> mulrfctE
  • scalrfunE -> scalrfctE
  • exprfunE -> exprfctE
  • valLr -> valR
  • valLr_fun -> valR_fun
  • valLrK -> valRK
  • oinv_valLr -> oinv_valR
  • valLr_inj_subproof -> valR_inj_subproof
  • valLr_surj_subproof -> valR_surj_subproof
• in measure.v:
  • measurable_bigcup -> bigcupT_measurable
  • measurable_bigcap -> bigcapT_measurable
  • measurable_bigcup_rat -> bigcupT_measurable_rat
• in lebesgue_measure.v:
  • emeasurable_bigcup -> bigcupT_emeasurable

Removed

• files posnum.v and nngnum.v (both subsumed by signed.v)
• in topology.v:
  • ltr_distlC, ler_distlC

[0.4.0] - 2022-03-08

Added

• in mathcomp_extra.v:
  • lemma all_sig2_cond
  • definition olift
  • lemmas obindEapp, omapEbind, omapEapp, oappEmap, omap_comp, oapp_comp, oapp_comp_f, olift_comp, compA, can_in_pcan, pcan_in_inj, can_in_comp, pcan_in_comp, ocan_comp, pred_omap, ocan_in_comp, eqbLR, eqbRL
  • definition opp_fun, notation \-
  • definition mul_fun, notation \*
  • definition max_fun, notation \max
  • lemmas gtr_opp, le_le_trans
  • notations eqLHS, eqRHS, leLHS, leRHS, ltLHS, lrRHS
  • inductive boxed
  • lemmas eq_big_supp, perm_big_supp_cond, perm_big_supp
  • lemmma mulr_ge0_gt0
  • lemmas lt_le, gt_ge
  • coercion pair_of_interval
  • lemmas ltBSide, leBSide
  • multirule lteBSide
  • lemmas ltBRight_leBLeft, leBRight_ltBLeft
  • multirule bnd_simp
  • lemmas itv_splitU1, itv_split1U
  • definition miditv
  • lemmas mem_miditv, miditv_bnd2, miditv_bnd1
  • lemmas predC_itvl, predC_itvr, predC_itv
• in boolp.v:
  • lemmas cid2, propeqP, funeqP, funeq2P, funeq3P, predeq2P, predeq3P
  • hint Prop_irrelevance
  • lemmas pselectT, eq_opE
  • definition classicType, canonicals classicType_eqType, classicType_choiceType, notation {classic ...}
  • definition eclassicType, canonicals eclassicType_eqType, eclassicType_choiceType, notation {eclassic ...}
  • definition canonical_of, notations canonical_, canonical, lemma canon
  • lemmas Peq, Pchoice, eqPchoice
  • lemmas contra_notT, contraPT, contraTP, contraNP, contraNP, contra_neqP, contra_eqP
  • lemmas forallPNP, existsPNP
  • module FunOrder, lemma lefP
  • lemmas meetfE and joinfE
• in classical_sets.v:
  • notations [set: ...], *`, `*
  • definitions setMR and setML, disj_set
  • coercion set_type, definition SigSub
  • lemmas set0fun, set_mem, mem_setT, mem_setK, set_memK, memNset, setTPn, in_set0, in_setT, in_setC, in_setI, in_setD, in_setU, in_setM, set_valP, set_true, set_false, set_andb, set_orb, fun_true, fun_false, set_mem_set, mem_setE, setDUK, setDUK, setDKU, setUv, setIv, setvU, setvI, setUCK, setUKC, setICK, setIKC, setDIK, setDKI, setI1, set1I, subsetT, disj_set2E, disj_set2P, disj_setPS, disj_set_sym, disj_setPCl, disj_setPCr, disj_setPLR, disj_setPRL, setF_eq0, subsetCl, subsetCr, subsetC2, subsetCP, subsetCPl, subsetCPr, subsetUl, subsetUr, setDidl, subIsetl, subIsetr, subDsetl, subDsetr setUKD, setUDK, setUIDK, bigcupM1l, bigcupM1r, pred_omapE, pred_omap_set
  • hints subsetUl, subsetUr, subIsetl, subIsetr, subDsetl, subDsetr
  • lemmas image2E
  • lemmas Iiota, ordII, IIord, ordIIK, IIordK
  • lemmas set_imfset, imageT
  • hints imageP, imageT
  • lemmas homo_setP, image_subP, image_sub, subset_set2
  • lemmas eq_preimage, comp_preimage, preimage_id, preimage_comp, preimage_setI_eq0, preimage0eq, preimage0, preimage10,
  • lemmas some_set0, some_set1, some_setC, some_setR, some_setI, some_setU, some_setD, sub_image_some, sub_image_someP, image_some_inj, some_set_eq0, some_preimage, some_image, disj_set_some
  • lemmas some_bigcup, some_bigcap, bigcup_set_type, bigcup_mkcond, bigcup_mkcondr, bigcup_mkcondl, bigcap_mkcondr, bigcap_mkcondl, bigcupDr, setD_bigcupl, bigcup_bigcup_dep, bigcup_bigcup, bigcupID. bigcapID
  • lemmas bigcup2inE, bigcap2, bigcap2E, bigcap2inE
  • lemmas bigcup_sub, sub_bigcap, subset_bigcup, subset_bigcap, bigcap_set_type, bigcup_pred
  • lemmas bigsetU_bigcup2, bigsetI_bigcap2
  • lemmas in1TT, in2TT, in3TT, inTT_bij
  • canonical option_pointedType
  • notations [get x | E], [get x : T | E]
  • variant squashed, notation $| ... |, tactic notation squash
  • definition unsquash, lemma unsquashK
  • module Empty that declares the type emptyType with the expected [emptyType of ...] notations
  • canonicals False_emptyType and void_emptyType
  • definitions no and any
  • lemmas empty_eq0
  • definition quasi_canonical_of, notations quasi_canonical_, quasi_canonical, lemma qcanon
  • lemmas choicePpointed, eqPpointed, Ppointed
  • lemmas trivIset_setIl, trivIset_setIr, sub_trivIset, trivIset_bigcup2
  • definition smallest
  • lemmas sub_smallest, smallest_sub, smallest_id
  • lemma and hint sub_gen_smallest
  • lemmas sub_smallest2r, sub_smallest2l
  • lemmas preimage_itv, preimage_itv_o_infty, preimage_itv_c_infty, preimage_itv_infty_o, preimage_itv_infty_c, notin_setI_preimage
  • definitions xsection, ysection
  • lemmas xsection0, ysection0, in_xsectionM, in_ysectionM, notin_xsectionM, notin_ysectionM, xsection_bigcup, ysection_bigcup, trivIset_xsection, trivIset_ysection, le_xsection, le_ysection, xsectionD, ysectionD
• in topology.v:
  • lemma filter_pair_set
  • definition prod_topo_apply
  • lemmas prod_topo_applyE, prod_topo_apply_continuous, hausdorff_product
  • lemmas closedC, openC
  • lemmas continuous_subspace_in
  • lemmasclosed_subspaceP, closed_subspaceW, closure_subspaceW
  • lemmas nbhs_subspace_subset, continuous_subspaceW, nbhs_subspaceT, continuous_subspaceT_for, continuous_subspaceT, continuous_open_subspace
  • globals subspace_filter, subspace_proper_filter
  • notation {within ..., continuous ...}
  • definitions compact_near, precompact, locally_compact
  • lemmas precompactE, precompact_subset, compact_precompact, precompact_closed
  • definitions singletons, equicontinuous, pointwise_precompact
  • lemmas equicontinuous_subset, equicontinuous_cts
  • lemmas pointwise_precomact_subset, pointwise_precompact_precompact uniform_pointwise_compact, compact_pointwise_precompact
  • lemmas compact_set1, uniform_set1, ptws_cvg_family_singleton, ptws_cvg_compact_family
  • lemmas connected1, connectedU
  • lemmas connected_component_sub, connected_component_id, connected_component_out, connected_component_max, connected_component_refl, connected_component_cover, connected_component_cover, connected_component_trans, same_connected_component
  • lemma continuous_is_cvg
  • lemmas uniform_limit_continuous, uniform_limit_continuous_subspace
• in normedtype.v
  • generalize IVT with subspace topology
  • lemmas abse_continuous, cvg_abse, is_cvg_abse, EFin_lim, near_infty_natSinv_expn_lt
• in reals.v:
  • lemmas sup_gt, inf_lt, ltr_add_invr
• in ereal.v:
  • lemmas esum_ninftyP, esum_pinftyP
  • lemmas addeoo, daddeoo
  • lemmas desum_pinftyP, desum_ninftyP
  • lemmas lee_pemull, lee_nemul, lee_pemulr, lee_nemulr
  • lemma fin_numM
  • definition mule_def, notation x *? y
  • lemma mule_defC
  • notations \* in ereal_scope, and ereal_dual_scope
  • lemmas mule_def_fin, mule_def_neq0_infty, mule_def_infty_neq0, neq0_mule_def
  • notation \- in ereal_scope and ereal_dual_scope
  • lemma fin_numB
  • lemmas mule_eq_pinfty, mule_eq_ninfty
  • lemmas fine_eq0, abse_eq0
  • lemmas EFin_inj, EFin_bigcup, EFin_setC, adde_gt0, mule_ge0_gt0, lte_mul_pinfty, lt0R, adde_defEninfty, lte_pinfty_eq, ge0_fin_numE, eq_pinftyP,
  • canonical mule_monoid
  • lemmas preimage_abse_pinfty, preimage_abse_ninfty
  • notation \-
  • lemmas fin_numEn, fin_numPn, oppe_eq0, ltpinfty_adde_def, gte_opp, gte_dopp, gt0_mulpinfty, lt0_mulpinfty, gt0_mulninfty, lt0_mulninfty, eq_infty, eq_ninfty, hasNub_ereal_sup, ereal_sup_EFin, ereal_inf_EFin, restrict_abse
  • canonical ereal_pointed
  • lemma seq_psume_eq0
  • lemmas lte_subl_addl, lte_subr_addl, lte_subel_addr, lte_suber_addr, lte_suber_addl, lee_subl_addl, lee_subr_addl, lee_subel_addr, lee_subel_addl, lee_suber_addr, lee_suber_addl
  • lemmas lte_dsubl_addl, lte_dsubr_addl, lte_dsubel_addr, lte_dsuber_addr, lte_dsuber_addl, lee_dsubl_addl, lee_dsubr_addl, lee_dsubel_addr, lee_dsubel_addl, lee_dsuber_addr, lee_dsuber_addl
  • lemmas realDe, realDed, realMe, nadde_eq0, padde_eq0, adde_ss_eq0, ndadde_eq0, pdadde_eq0, dadde_ss_eq0, mulrpinfty_real, mulpinftyr_real, mulrninfty_real, mulninftyr_real, mulrinfty_real
• in sequences.v:
  • lemmas ereal_cvgM_gt0_pinfty, ereal_cvgM_lt0_pinfty, ereal_cvgM_gt0_ninfty, ereal_cvgM_lt0_ninfty, ereal_cvgM
  • definition eseries with notation [eseries E]_n
    • lemmas eseriesEnat, eseriesEord, eseriesSr, eseriesS, eseriesSB, eseries_addn, sub_eseries_geq, sub_eseries, sub_double_eseries, eseriesD
  • definition etelescope
  • lemmas ereal_cvgB, nondecreasing_seqD, lef_at
  • lemmas lim_mkord, ereal_pseries_mkcond, ereal_pseries_sum
  • definition sdrop
  • lemmas has_lbound_sdrop, has_ubound_sdrop
  • definitions sups, infs
  • lemmas supsN, infsN, nonincreasing_sups, nondecreasing_infs, is_cvg_sups, is_cvg_infs, infs_le_sups, cvg_sups_inf, cvg_infs_sup, sups_preimage, infs_preimage, bounded_fun_has_lbound_sups, bounded_fun_has_ubound_infs
  • definitions lim_sup, lim_inf
  • lemmas lim_infN, lim_supE, lim_infE, lim_inf_le_lim_sup, cvg_lim_inf_sup, cvg_lim_infE, cvg_lim_supE, cvg_sups, cvg_infs, le_lim_supD, le_lim_infD, lim_supD, lim_infD
  • definitions esups, einfs
  • lemmas esupsN, einfsN, nonincreasing_esups, nondecreasing_einfs, einfs_le_esups, cvg_esups_inf, is_cvg_esups, cvg_einfs_sup, is_cvg_einfs, esups_preimage, einfs_preimage
  • definitions elim_sup, elim_inf
  • lemmas elim_infN, elim_supN, elim_inf_sup, elim_inf_sup, cvg_ninfty_elim_inf_sup, cvg_ninfty_einfs, cvg_ninfty_esups, cvg_pinfty_einfs, cvg_pinfty_esups, cvg_esups, cvg_einfs, cvg_elim_inf_sup, is_cvg_elim_infE, is_cvg_elim_supE
  • lemmas elim_inf_shift, elim_sup_le_cvg
• in derive.v
  • lemma MVT_segment
  • lemma derive1_cst
• in realfun.v:
  • lemma continuous_subspace_itv
• in esum.v (was csum.v):
  • lemmas sum_fset_set, esum_ge, esum0, le_esum, eq_esum, esumD, esum_mkcond, esum_mkcondr, esum_mkcondl, esumID, esum_sum, esum_esum, lee_sum_fset_nat, lee_sum_fset_lim, ereal_pseries_esum, reindex_esum, esum_pred_image, esum_set_image, esum_bigcupT
• in cardinality.v:
  • notations #>=, #=, #!=
  • scope card_scope, delimiter card
  • notation infinite_set
  • lemmas injPex, surjPex, bijPex, surjfunPex, injfunPex
  • lemmas inj_card_le, pcard_leP, pcard_leTP, pcard_injP, ppcard_leP
  • lemmas pcard_eq, pcard_eqP, card_bijP, card_eqVP, card_set_bijP
  • lemmas ppcard_eqP, card_eqxx, inj_card_eq, card_some, card_image, card_imsub
  • hint card_eq00
  • lemmas empty_eq0, card_le_emptyl, card_le_emptyr
  • multi-rule emptyE_subdef
  • lemmas card_eq_le, card_eqPle, card_leT, card_image_le
  • lemmas card_le_eql, card_le_eqr, card_eql, card_eqr, card_ge_image, card_le_image, card_le_image2, card_eq_image, card_eq_imager, card_eq_image2
  • lemmas card_ge_some, card_le_some, card_le_some2, card_eq_somel, card_eq_somer, card_eq_some2
  • lemmas card_eq_emptyr, card_eq_emptyl, emptyE
  • lemma and hint card_setT
  • lemma and hint card_setT_sym
  • lemmas surj_card_ge, pcard_surjP, pcard_geP, ocard_geP, pfcard_geP
  • lemmas ocard_eqP, oocard_eqP, sub_setP, card_subP
  • lemmas eq_countable, countable_set_countMixin, countableP, sub_countable
  • lemmas card_II, finite_fsetP, finite_subfsetP, finite_seqP, finite_fset, finite_finpred, finite_finset, infiniteP, finite_setPn
  • lemmas card_le_finite, finite_set_leP, card_ge_preimage, eq_finite_set, finite_image
  • lemma and hint finite_set1
  • lemmas finite_setU, finite_set2, finite_set3, finite_set4, finite_set5, finite_set6, finite_set7, finite_setI, finite_setIl, finite_setIr, finite_setM, finite_image2, finite_image11
  • definition fset_set
  • lemmas fset_setK, in_fset_set, fset_set0, fset_set1, fset_setU, fset_setI, fset_setU1, fset_setD, fset_setD1, fset_setM
  • definitions fst_fset, snd_fset, notations .`1, .`2
  • lemmas finite_set_fst, finite_set_snd, bigcup_finite, finite_setMR, finite_setML, fset_set_II, set_fsetK, fset_set_inj, bigsetU_fset_set, bigcup_fset_set, bigsetU_fset_set_cond, bigcup_fset_set_cond, bigsetI_fset_set, bigcap_fset_set, super_bij, card_eq_fsetP, card_IID, finite_set_bij
  • lemmas countable1, countable_fset
  • lemma and hint countable_finpred
  • lemmas eq_card_nat
  • canonical rat_pointedType
  • lemmas infinite_rat, card_rat, choicePcountable, eqPcountable, Pcountable, bigcup_countable, countableMR, countableM, countableML, infiniteMRl, cardMR_eq_nat
  • mixin FiniteImage, structure FImFun, notations {fumfun ... >-> ...}, [fimfun of ...], hint fimfunP
  • lemma and hint fimfun_inP
  • definitions fimfun, fimfun_key, canonical fimfun_keyed
  • definitions fimfun_Sub_subproof, fimfun_Sub
  • lemmas fimfun_rect, fimfun_valP, fimfuneqP
  • definitions and canonicals fimfuneqMixin, fimfunchoiceMixin
  • lemma finite_image_cst, cst_fimfun_subproof, fimfun_cst
  • definition cst_fimfun
  • lemma comp_fimfun_subproof
  • lemmas fimfun_zmod_closed, fimfunD, fimfunN, fimfunB, fimfun0, fimfun_sum
  • canonicals fimfun_add, fimfun_zmod, fimfun_zmodType
  • definition fimfun_zmodMixin
• in measure.v:
  • definitions setC_closed, setI_closed, setU_closed, setD_closed, setDI_closed, fin_bigcap_closed, finN0_bigcap_closed, fin_bigcup_closed, semi_setD_closed, ndseq_closed, trivIset_closed, fin_trivIset_closed, set_ring, sigma_algebra, dynkin, monotone_classes
  • notations <<m D, G >>, <<m G >>, <<s D, G>>, <<s G>>, <<d G>>, <<r G>>, <<fu G>>
  • lemmas fin_bigcup_closedP, finN0_bigcap_closedP, sedDI_closedP, sigma_algebra_bigcap, sigma_algebraP
  • lemma and hint smallest_sigma_algebra
  • lemmas sub_sigma_algebra2, sigma_algebra_id, sub_sigma_algebra, sigma_algebra0, sigma_algebraD, sigma_algebra_bigcup
  • lemma and hint smallest_setring, lemma and hint setring0
  • lemmas sub_setring2, setring_id, sub_setring, setringDI, setringU, setring_fin_bigcup, monotone_class_g_salgebra
  • lemmas smallest_monotone_classE, monotone_class_subset, dynkinT, dynkinC, dynkinU, dynkin_monotone, dynkin_g_dynkin, sigma_algebra_dynkin, dynkin_setI_bigsetI, dynkin_setI_sigma_algebra, setI_closed_gdynkin_salgebra
  • factories isRingOfSets, isAlgebraOfSets
  • lemmas fin_bigcup_measurable, fin_bigcap_measurable, sigma_algebra_measurable, sigma_algebraC
  • definition measure_restr, lemma measure_restrE
  • definition g_measurableType
  • lemmas measurable_g_measurableTypeE
  • lemmas measurable_fun_id, measurable_fun_comp, eq_measurable_fun, measurable_fun_cst, measurable_funU, measurable_funS, measurable_fun_ext, measurable_restrict
  • definitions preimage_class and image_class
  • lemmas preimage_class_measurable_fun, sigma_algebra_preimage_class, sigma_algebra_image_class, sigma_algebra_preimage_classE, measurability
  • definition sub_additive
  • lemma semi_additiveW
  • lemmas content_fin_bigcup, measure_fin_bigcup, measure_bigsetU_ord_cond, measure_bigsetU_ord,
  • coercion measure_to_nadditive_measure
  • lemmas measure_semi_bigcup, measure_bigcup
  • hint measure_ge0
  • lemma big_trivIset
  • defintion covered_by
  • module SetRing
    • lemmas ring_measurableE, ring_fsets
    • definition decomp
    • lemmas decomp_triv, decomp_triv, decomp_neq0, decomp_neq0, decomp_measurable, cover_decomp, decomp_sub, decomp_set0, decomp_set0
    • definition measure
    • lemma Rmu_fin_bigcup, RmuE, Rmu0, Rmu_ge0, Rmu_additive, Rmu_additive_measure
    • canonical measure_additive_measure
  • lemmas covered_byP, covered_by_finite, covered_by_countable, measure_le0, content_sub_additive, content_sub_fsum, content_ring_sup_sigma_additive, content_ring_sigma_additive, ring_sigma_sub_additive, ring_sigma_additive, measure_sigma_sub_additive, measureIl, measureIr, subset_measure0, measureUfinr, measureUfinl, eq_measureU, null_set_setU
  • lemmas g_salgebra_measure_unique_trace, g_salgebra_measure_unique_cover, g_salgebra_measure_unique, measure_unique, measurable_mu_extE, Rmu_ext, measurable_Rmu_extE, sub_caratheodory
  • definition Hahn_ext, canonical Hahn_ext_measure, lemma Hahn_ext_sigma_finite, Hahn_ext_unique, caratheodory_measurable_mu_ext
  • definitions preimage_classes, prod_measurable, prod_measurableType
  • lemmas preimage_classes_comp, measurableM, measurable_prod_measurableType, measurable_prod_g_measurableTypeR, measurable_prod_g_measurableType, prod_measurable_funP, measurable_fun_prod1, measurable_fun_prod2
• in functions.v:
  • definitions set_fun, set_inj
  • mixin isFun, structure Fun, notations {fun ... >-> ...}, [fun of ...]
    • field funS declared as a hint
  • mixin OInv, structure OInversible, notations {oinv ... >-> ...}, [oinv of ...], 'oinv_ ...
  • structure OInvFun, notations {oinvfun ... >-> ...}, [oinvfun of ...]
  • mixin OInv_Inv, factory Inv, structure Inversible, notations {inv ... >-> ...}, [inv of ...], notation ^-1
  • structure InvFun, notations {invfun ... >-> ...}, [invfun of ...]
  • mixin OInv_CanV with field oinvK declared as a hint, factory OCanV
  • structure Surject, notations {surj ... >-> ...}, [surj of ...]
  • structure SurjFun, notations {surjfun ... >-> ...}, [surjfun of ...]
  • structure SplitSurj, notations {splitsurj ... >-> ...}, [splitsurj of ...]
  • structure SplitSurjFun, notations {splitsurjfun ... >-> ...}, [splitsurjfun of ...]
  • mixin OInv_Can with field funoK declared as a hint, structure Inject, notations {inj ... >-> ...}, [inj of ...]
  • structure InjFun, notations {injfun ... >-> ...}, [injfun of ...]
  • structure SplitInj, notations {splitinj ... >-> ...}, [splitinj of ...]
  • structure SplitInjFun, notations {splitinjfun ... >-> ...}, [splitinjfun of ...]
  • structure Bij, notations {bij ... >-> ...}, [bij of ...]
  • structure SplitBij, notations {splitbij ... >-> ...}, [splitbij of ...]
  • module ShortFunSyntax for shorter notations
  • notation 'funS_ ...
  • definition and hint fun_image_sub
  • definition and hint mem_fun
  • notation 'mem_fun_ ...
  • lemma some_inv
  • notation 'oinvS_ ...
  • variant oinv_spec, lemma and hint oinvP
  • notation 'oinvP_ ...
  • lemma and hint oinvT, notation 'oinvT_ ...
  • lemma and hint invK, notation 'invK_ ...
  • lemma and hint invS, notation 'invS_ ...
  • notation 'funoK_ ...
  • definition inj and notation 'inj_ ...
  • definition and hint inj_hint
  • lemma and hint funK, notation 'funK_ ...
  • lemma funP
  • factories Inv_Can, Inv_CanV
  • lemmas oinvV, surjoinv_inj_subproof, injoinv_surj_subproof, invV, oinv_some, some_canV_subproof, some_fun_subproof, inv_oapp, oinv_oapp, inv_oappV, oapp_can_subproof, oapp_surj_subproof, oapp_fun_subproof, inv_obind, oinv_obind, inv_obindV, oinv_comp, some_comp_inv, inv_comp, comp_can_subproof, comp_surj_subproof,
  • notation 'totalfun_ ...
  • lemmas oinv_olift, inv_omap, oinv_omap, omapV
  • factories canV, OInv_Can2, OCan2, Can, Inv_Can2, Can2, SplitInjFun_CanV, BijTT
  • lemmas surjective_oinvK, surjective_oinvS, coercion surjective_ocanV
  • definition and coercion surjection_of_surj, lemma Psurj, coercion surjection_of_surj
  • lemma oinv_surj, lemma and hint surj, notation 'surj_
  • definition funin, lemma set_fun_image, notation [fun ... in ...]
  • definition split_, lemmas splitV, splitis_inj_subproof, splitid, splitsurj_subproof, notation 'split_, split
  • factories Inj, SurjFun_Inj, SplitSurjFun_Inj
  • lemmas Pinj, Pfun, injPfun, funPinj, funPsurj, surjPfun, Psplitinj, funPsplitinj, PsplitinjT, funPsplitsurj, PsplitsurjT
  • definition unbind
  • lemmas unbind_fun_subproof, oinv_unbind, inv_unbind_subproof, inv_unbind, unbind_inj_subproof, unbind_surj_subproof, odflt_unbind, oinv_val, val_bij_subproof, inv_insubd
  • definition to_setT, lemma inv_to_setT
  • definition subfun, lemma subfun_inj
  • lemma subsetW, definition subsetCW
  • lemmas subfun_imageT, subfun_inv_subproof
  • definition seteqfun, lemma seteqfun_can2_subproof
  • definitions incl, eqincl, lemma eqincl_surj, notation inclT
  • definitions mkfun, mkfun_fun
  • definition set_val, lemmas oinv_set_val, set_valE
  • definition ssquash
  • lemma set0fun_inj
  • definitions finset_val, val_finset
  • lemmas finset_valK, val_finsetK
  • definition glue, glue1, glue2, lemmas glue_fun_subproof, oinv_glue, some_inv_glue_subproof, inv_glue, glueo_can_subproof, glue_canv_subproof
  • lemmas inv_addr, addr_can2_subproof
  • lemmas empty_can_subproof, empty_fun_subproof, empty_canv_subproof
  • lemmas subl_surj, subr_surj, surj_epi, epiP, image_eq, oinv_image_sub, oinv_Iimage_sub, oinv_sub_image, inv_image_sub, inv_Iimage_sub, inv_sub_image, reindex_bigcup, reindex_bigcap, bigcap_bigcup, trivIset_inj, set_bij_homo
  • definition and hint fun_set_bij
  • coercion set_bij_bijfun
  • definition and coercion bij_of_set_bijection
  • lemma and hint bij, notation 'bij_
  • definition bijection_of_bijective, lemmas PbijTT, setTT_bijective, lemma and hint bijTT, notation 'bijTT_
  • lemmas patchT, patchN, patchC, patch_inj_subproof, preimage_restrict, comp_patch, patch_setI, patch_set0, patch_setT, restrict_comp
  • definitions sigL, sigLfun, valL_, valLfun_
  • lemmas sigL_isfun, valL_isfun, sigLE, eq_sigLP, eq_sigLfunP, sigLK, valLK, valLfunK, sigL_valL, sigL_valLfun\, sigL_restrict, image_sigL, eq_restrictP
  • notations 'valL_ ..., 'valLfun_ ..., valL
  • definitions sigR, valLr, valLr_fun
  • lemmas sigRK, sigR_funK, valLrP, valLrK
  • lemmas oinv_sigL, sigL_inj_subproof, sigL_surj_subproof, oinv_sigR, sigR_inj_subproof, sigR_surj_subproof, sigR_some_inv, inv_sigR, sigL_some_inv, inv_sigL, oinv_valL, oapp_comp_x, valL_inj_subproof, valL_surj_subproof, valL_some_inv, inv_valL, sigL_injP, sigL_surjP, sigL_funP, sigL_bijP, valL_injP, valL_surjP, valLfunP, valL_bijP
  • lemmas oinv_valLr, valLr_inj_subproof, valLr_surj_subproof
  • definitions sigLR, valLR, valLRfun, lemmas valLRE, valLRfunE, sigL2K, valLRK, valLRfun_inj, sigLR_injP, valLR_injP, sigLR_surjP, valLR_surjP, sigLR_bijP, sigLRfun_bijP, valLR_bijP, subsetP
  • new lemmas eq_set_bijLR, eq_set_bij, bij_omap, bij_olift, bij_sub_sym, splitbij_sub_sym, set_bij00, bij_subl, bij_sub, splitbij_sub, can2_bij, bij_sub_setUrl, bij_sub_setUrr, bij_sub_setUrr, bij_sub_setUlr
  • definition pinv_, lemmas injpinv_surj, injpinv_image, injpinv_bij, surjpK, surjpinv_image_sub, surjpinv_inj, surjpinv_bij, bijpinv_bij, pPbij_, pPinj_, injpPfun_, funpPinj_
• in fsbigop.v:
  • notations \big[op/idx]_(i \in A) f i, \sum_(i \in A) f i
  • lemma finite_index_key
  • definition finite_support
  • lemmas in_finite_support, no_finite_support, eq_finite_support
  • variant finite_support_spec
  • lemmas finite_supportP, eq_fsbigl, eq_fsbigr, fsbigTE, fsbig_mkcond, fsbig_mkcondr, fsbig_mkcondl, bigfs, fsbigE, fsbig_seq, fsbig1, fsbig_dflt, fsbig_widen, fsbig_supp, fsbig_fwiden, fsbig_set0, fsbig_set1, full_fsbigID, fsbigID, fsbigU, fsbigU0, fsbigD1, full_fsbig_distrr, fsbig_distrr, mulr_fsumr, mulr_fsuml, fsbig_ord, fsbig_finite, reindex_fsbig, fsbig_image, reindex_inside, reindex_fsbigT, notation reindex_inside_setT
  • lemmas ge0_mule_fsumr, ge0_mule_fsuml, fsbigN1, fsume_ge0, fsume_le0, fsume_gt0, fsume_lt0, pfsume_eq0, fsbig_setU, pair_fsum, exchange_fsum, fsbig_split
• in set_interval.v:
  • definition neitv
  • lemmas neitv_lt_bnd, set_itvP, subset_itvP, set_itvoo, set_itvco, set_itvcc, set_itvoc, set_itv1, set_itvoo0, set_itvoc0, set_itvco0, set_itv_infty_infty, set_itv_o_infty, set_itv_c_infty, set_itv_infty_o, set_itv_infty_c, set_itv_pinfty_bnd, set_itv_bnd_ninfty
  • multirules set_itv_infty_set0, set_itvE
  • lemmas setUitv1, setU1itv
  • lemmas neitvE, neitvP, setitv0
  • lemmas set_itvI
  • lemmas and hints has_lbound_itv, has_ubound_itv, hasNlbound_itv, hasNubound_itv, has_sup_half, has_inf_half
  • lemmas opp_itv_bnd_infty, opp_itvoo, sup_itv, inf_itv, sup_itvcc, inf_itvcc setCitvl, setCitvr, setCitv
  • lemmas set_itv_splitD, set_itvK, RhullT, RhullK, itv_c_inftyEbigcap, itv_bnd_inftyEbigcup, itv_o_inftyEbigcup, set_itv_setT, set_itv_ge
  • definitions conv, factor
  • lemmas conv_id, convEl, convEr, conv10, conv0, conv1, conv_sym, conv_flat, factorl, factorr, factor_flat, mem_1B_itvcc, factorK, convK, conv_inj, conv_bij, factor_bij, leW_conv, leW_factor, le_conv, le_factor, lt_conv, lt_factor
  • definition ndconv
  • lemmas ndconvE, conv_itv_bij, conv_itv_bij, factor_itv_bij, mem_conv_itv, mem_factor_itv, mem_conv_itvcc, range_conv, range_factor, Rhull_smallest, le_Rhull, neitv_Rhull, Rhull_involutive
  • coercion ereal_of_itv_bound
  • lemmas le_bnd_ereal, lt_ereal_bnd, neitv_bnd1, neitv_bnd2, Interval_ereal_mem, ereal_mem_Interval, trivIset_set_itv_nth
  • definition disjoint_itv
  • lemmas disjoint_itvxx, lt_disjoint, disjoint_neitv, disj_itv_Rhull
• new file numfun.v
  • lemmas restrict_set0, restrict_ge0, erestrict_set0, erestrict_ge0, ler_restrict, lee_restrict
  • definition funenng and notation ^\+, definition funennp and notation ^\-
  • lemmas and hints funenng_ge0, funennp_ge0
  • lemmas funenngN, funennpN, funenng_restrict, funennp_restrict, ge0_funenngE, ge0_funennpE, le0_funenngE, le0_funennpE, gt0_funenngM, gt0_funennpM, lt0_funenngM, lt0_funennpM, fune_abse, funenngnnp, add_def_funennpg, funeD_Dnng, funeD_nngD
  • definition indic and notation \1_
  • lemmas indicE, indicT, indic0, indic_restrict, restrict_indic, preimage_indic, image_indic, image_indic_sub
• in trigo.v:
  • lemmas acos1, acos0, acosN1, acosN, cosKN, atan0, atan1
• new file lebesgue_measure.v
• new file lebesgue_integral.v

Changed

• in boolp.v:
  • equality_mixin_of_Type, choice_of_Type -> see classicalType
• in topology.v:
  • generalize connected_continuous_connected, continuous_compact
  • arguments of subspace
  • definition connected_component
• in sequences.v:
  • \sum notations for extended real numbers now in ereal_scope
  • lemma ereal_cvg_sub0 is now an equivalence
• in derive.v:
  • generalize EVT_max, EVT_min, Rolle, MVT, ler0_derive1_nincr, le0r_derive1_ndecr with subspace topology
  • implicits of cvg_at_rightE, cvg_at_leftE
• in trigo.v:
  • the realType argument of pi is implicit
  • the printed type of acos, asin, atan is R -> R
• in esum.v (was csum.v):
  • lemma esum_ge0 has now a weaker hypothesis
• notation `I_ moved from cardinality.v to classical_sets.v
• moved from classical_types.v to boolp.v:
  • definitions gen_eq and gen_eqMixin, lemma gen_eqP
  • canonicals arrow_eqType, arrow_choiceType
  • definitions dep_arrow_eqType, dep_arrow_choiceClass, dep_arrow_choiceType
  • canonicals Prop_eqType, Prop_choiceType
• in classical_sets.v:
  • arguments of preimage
  • [set of f] becomes range f (the old notation is still available but is displayed as the new one, and will be removed in future versions)
• in cardinality.v:
  • definition card_eq now uses {bij ... >-> ...}
  • definition card_le now uses {injfun ... >-> ...}
  • definition set_finite changed to finite_set
  • definition card_leP now uses reflect
  • definition card_le0P now uses reflect
  • definition card_eqP now uses reflect
  • statement of theorem Cantor_Bernstein
  • lemma subset_card_le does not require finiteness of rhs anymore
  • lemma surjective_card_le does not require finiteness of rhs anymore and renamed to surj_card_ge
  • lemma card_le_diff does not require finiteness of rhs anymore and renamed to card_le_setD
  • lemma card_eq_sym now an equality
  • lemma card_eq0 now an equality
  • lemmas card_le_II and card_eq_II now equalities
  • lemma countable_injective renamed to countable_injP and use reflect
  • lemmas II0, II1, IIn_eq0 moved to classical_sets.v
  • lemma II_recr renamed to IIS and moved to classical_sets.v
  • definition surjective moved to functions.v and renamed set_surj
  • definition set_bijective moved to functions.v and changed to set_bij
  • lemma surjective_id moved to functions.v and renamed surj_id
  • lemma surjective_set0 moved to functions.v and renamed surj_set0
  • lemma surjectiveE moved to functions.v and renamed surjE
  • lemma surj_image_eq moved to functions.v
  • lemma can_surjective moved to functions.v and changed to can_surj
  • lemma surjective_comp moved to functions.v and renamed surj_comp
  • lemma set_bijective1 moved to functions.v and renamed eq_set_bijRL
  • lemma set_bijective_image moved to functions.v and renamed inj_bij
  • lemma set_bijective_subset moved to functions.v and changed to bij_subr
  • lemma set_bijective_comp moved to functions.v and renamed set_bij_comp
  • definition inverse changed to pinv_, see functions.v
  • lemma inj_of_bij moved to functions.v and renamed to set_bij_inj
  • lemma sur_of_bij moved to functions.v and renamed to set_bij_surj
  • lemma sub_of_bij moved to functions.v and renamed to set_bij_sub
  • lemma set_bijective_D1 moved to functions.v and renamed to bij_II_D1
  • lemma injective_left_inverse moved to functions.v and changed to pinvKV
  • lemma injective_right_inverse moved to functions.v and changed to pinvK
  • lemmas image_nat_maximum, fset_nat_maximum moved to mathcomp_extra.v
  • lemmas enum0, enum_recr moved to mathcomp_extra.v and renamed to enum_ord0, enum_ordS
  • lemma in_inj_comp moved to mathcomp_extra.v
• from cardinality.v to classical_sets.v:
  • eq_set0_nil -> set_seq_eq0
  • eq_set0_fset0 -> set_fset_eq0
• in measure.v:
  • definition bigcup2, lemma bigcup2E moved to classical_sets.v
  • mixin isSemiRingOfSets and isRingOfSets changed
  • types semiRingOfSetsType, ringOfSetsType, algebraOfSetsType, measurableType now pointed types
  • definition measurable_fun changed
  • definition sigma_sub_additive changed and renamed to sigma_subadditive
  • record AdditiveMeasure.axioms
  • lemmas measure_ge0
  • record Measure.axioms
  • definitions seqDU, seqD, lemma and hint trivIset_seqDU, lemmas bigsetU_seqDU, seqDU_bigcup_eq, seqDUE, trivIset_seqD, bigsetU_seqD, setU_seqD, eq_bigsetU_seqD, eq_bigcup_seqD, eq_bigcup_seqD_bigsetU moved to sequences.v
  • definition negligibleP weakened to additive measures
  • lemma measure_negligible
  • definition caratheodory_measurable and caratheodory_type weakened from outer measures to functions
  • lemma caratheodory_measure_ge0 does take a condition anymore
  • definitions measurable_cover and mu_ext, canonical outer_measure_of_measure weakened to semiRingOfSetsType
• in ereal.v:
  • lemmas abse_ge0, gee0_abs, gte0_abs, lee0_abs, lte0_abs, mulN1e, muleN1 are generalized from realDomainType to numDomainType
• moved from normedtype.v to mathcomp_extra.v:
  • lemmas ler_addgt0Pr, ler_addgt0Pl, in_segment_addgt0Pr, in_segment_addgt0Pl,
• moved from posnum.v to mathcomp_extra.v:
  • lemma splitr
• moved from measure.v to sequences.v
  • lemma cvg_geometric_series_half
  • lemmas realDe, realDed, realMe, nadde_eq0, padde_eq0, adde_ss_eq0, ndadde_eq0, pdadde_eq0, dadde_ss_eq0, mulrpinfty_real, mulpinftyr_real, mulrninfty_real, mulninftyr_real, mulrinfty_real
• moved from topology.v to functions.v
  • section function_space (defintion cst, definition fct_zmodMixin, canonical fct_zmodType, definition fct_ringMixin, canonical fct_ringType, canonical fct_comRingType, definition fct_lmodMixin, canonical fct_lmodType, lemma fct_lmodType)
  • lemmas addrfunE, opprfunE, mulrfunE, scalrfunE, cstE, exprfunE, compE
  • definition fctE
• moved from classical_sets.v to functions.v
  • definition patch, notation restrict and f \_ D

Renamed

• in topology.v:
  • closedC -> open_closedC
  • openC -> closed_openC
  • cvg_restrict_dep -> cvg_sigL
• in classical_sets.v:
  • mkset_nil -> set_nil
• in cardinality.v:
  • card_le0x -> card_ge0
  • card_eq_sym -> card_esym
  • set_finiteP -> finite_setP
  • set_finite0 -> finite_set0
  • set_finite_seq -> finite_seq
  • set_finite_countable -> finite_set_countable
  • subset_set_finite -> sub_finite_set
  • set_finite_preimage -> finite_preimage
  • set_finite_diff -> finite_setD
  • countably_infinite_prod_nat -> card_nat2
• file csum.v renamed to esum.v with the following renamings:
  • \csum -> \esum
  • csum -> esum
  • csum0 -> esum_set0
  • csum_ge0 -> esum_ge0
  • csum_fset -> esum_fset
  • csum_image -> esum_image
  • csum_bigcup -> esum_bigcup
• in ereal.v:
  • lte_subl_addl -> lte_subel_addl
  • lte_subr_addr -> lte_suber_addr
  • lte_dsubl_addl -> lte_dsubel_addl
  • lte_dsubr_addr -> lte_dsuber_addr

Removed

• in ereal.v:
  • lemmas esum_fset_ninfty, esum_fset_pinfty
  • lemmas desum_fset_pinfty, desum_fset_ninfty
  • lemmas big_nat_widenl, big_geq_mkord
• in csum.v:
  • lemmas fsets_img, fsets_ord, fsets_ord_nat, fsets_ord_subset, csum_bigcup_le, le_csum_bigcup
• in classical_sets.v:
  • lemma subsetU
  • definition restrict_dep, extend_up, lemma restrict_depE
• in cardinality.v:
  • lemma surjective_image, surjective_image_eq0
  • lemma surjective_right_inverse,
  • lemmas card_le_surj, card_eq00
  • lemmas card_eqTT, card_eq_II, card_eq_le, card_leP
  • lemmas set_bijective_inverse, countable_trans, set_bijective_U1, set_bijective_cyclic_shift, set_bijective_cyclic_shift_simple, set_finite_bijective, subset_set_finite_card_le, injective_set_finite_card_le, injective_set_finite, injective_card_le, surjective_set_finite_card_le, set_finite_inter_set0_union, ex_in_D.
  • definitions min_of_D, min_of_D_seq, infsub_enum
  • lemmas min_of_D_seqE, increasing_infsub_enum, sorted_infsub_enum, injective_infsub_enum, subset_infsub_enum, infinite_nat_subset_countable
  • definition enumeration
  • lemmas enumeration_id, enumeration_set0, ex_enum_notin
  • defnitions min_of_e, min_of_e_seq, smallest_of_e, enum_wo_rep
  • lemmas enum_wo_repE, min_of_e_seqE, smallest_of_e_notin_enum_wo_rep, injective_enum_wo_rep, surjective_enum_wo_rep, set_bijective_enum_wo_rep, enumeration_enum_wo_rep, countable_enumeration
  • definition nat_of_pair
  • lemmas nat_of_pair_inj, countable_prod_nat
• in measure.v:
  • definition diff_fsets
  • lemmas semiRingOfSets_measurableI, semiRingOfSets_measurableD, semiRingOfSets_diff_fsetsE, semiRingOfSets_diff_fsets_disjoint
  • definition uncurry
• in sequences.v:
  • lemmas leq_fact, prod_rev, fact_split (now in MathComp)
• in boolp.v
  • module BoolQuant with notations `[forall x P] and `[exists x P] (subsumed by `[< >])
  • definition xchooseb
  • lemmas existsPP, forallPP, existsbP, forallbP, forallbE, existsp_asboolP, forallp_asboolP, xchoosebP, imsetbP
• in normedtype.v:
  • lemmas nbhs_pinfty_gt_pos, nbhs_pinfty_ge_pos, nbhs_ninfty_lt_pos, nbhs_ninfty_le_pos

[0.3.13] - 2022-01-24

Added

• in topology.v:
  • definitions kolmogorov_space, accessible_space
  • lemmas accessible_closed_set1, accessible_kolmogorov
  • lemma filter_pair_set
  • definition prod_topo_apply
  • lemmas prod_topo_applyE, prod_topo_apply_continuous, hausdorff_product
• in ereal.v:
  • lemmas lee_pemull, lee_nemul, lee_pemulr, lee_nemulr
  • lemma fin_numM
  • definition mule_def, notation x *? y
  • lemma mule_defC
  • notations \* in ereal_scope, and ereal_dual_scope
  • lemmas mule_def_fin, mule_def_neq0_infty, mule_def_infty_neq0, neq0_mule_def
  • notation \- in ereal_scope and ereal_dual_scope
  • lemma fin_numB
  • lemmas mule_eq_pinfty, mule_eq_ninfty
  • lemmas fine_eq0, abse_eq0
• in sequences.v:
  • lemmas ereal_cvgM_gt0_pinfty, ereal_cvgM_lt0_pinfty, ereal_cvgM_gt0_ninfty, ereal_cvgM_lt0_ninfty, ereal_cvgM

Changed

• in topology.v:
  • renamed and generalized setC_subset_set1C implication to equivalence subsetC1
• in ereal.v:
  • lemmas ereal_sup_gt, ereal_inf_lt now use exists2
• notation \* moved from realseq.v to topology.v

Renamed

• in `topology.v:
  • hausdorff -> hausdorff_space

Removed

• in realseq.v:
  • notation \-

Infrastructure

• add .dir-locals.el for company-coq symbols

[0.3.12] - 2021-12-29

Added

• in boolp.v:
  • lemmas not_True, not_False
• in classical_sets.v:
  • lemma setDIr
  • lemmas setMT, setTM, setMI
  • lemmas setSM, setM_bigcupr, setM_bigcupl
  • lemmas cover_restr, eqcover_r
  • lemma notin_set
• in reals.v:
  • lemma has_ub_lbN
• in ereal.v:
  • lemma onee_eq0
  • lemma EFinB
  • lemmas mule_eq0, mule_lt0_lt0, mule_gt0_lt0, mule_lt0_gt0, pmule_rge0, pmule_lge0, nmule_lge0, nmule_rge0, pmule_rgt0, pmule_lgt0, nmule_lgt0, nmule_rgt0
  • lemmas muleBr, muleBl
  • lemma eqe_absl
  • lemma lee_pmul
  • lemmas fin_numElt, fin_numPlt
• in topology.v
  • lemmas cstE, compE, opprfunE, addrfunE, mulrfunE, scalrfunE, exprfunE
  • multi-rule fctE
  • lemmas within_interior, within_subset, withinE, fmap_within_eq
  • definitions subspace, incl_subspace.
  • canonical instances of pointedType, filterType, topologicalType, uniformType and pseudoMetricType on subspace.
  • lemmas nbhs_subspaceP, nbhs_subspace_in, nbhs_subspace_out, subspace_cvgP, subspace_continuousP, subspace_eq_continuous, nbhs_subspace_interior, nbhs_subspace_ex, incl_subspace_continuous, open_subspace1out, open_subspace_out, open_subspaceT, open_subspaceIT, open_subspaceTI, closed_subspaceT, open_subspaceP, open_subspaceW, subspace_hausdorff, and compact_subspaceIP.
• in normedtype.v
  • lemmas continuous_shift, continuous_withinNshiftx
  • lemmas bounded_fun_has_ubound, bounded_funN, bounded_fun_has_lbound, bounded_funD
• in derive.v
  • lemmas derive1_comp, derivable_cst, derivable_id, trigger_derive`
  • instances is_derive_id, is_derive_Nid
• in sequences.v:
  • lemmas cvg_series_bounded, cvg_to_0_linear, lim_cvg_to_0_linear.
  • lemma cvg_sub0
  • lemma cvg_zero
  • lemmas ereal_cvg_abs0, ereal_cvg_sub0, ereal_squeeze
  • lemma ereal_is_cvgD
• in measure.v:
  • hints for measurable0 and measurableT
• file realfun.v:
  • lemma is_derive1_caratheodory, is_derive_0_is_cst
  • instance is_derive1_comp
  • lemmas is_deriveV, is_derive_inverse
• new file nsatz_realType
• new file exp.v
  • lemma normr_nneg (hint)
  • definitions pseries, pseries_diffs
  • facts is_cvg_pseries_inside_norm, is_cvg_pseries_inside
  • lemmas pseries_diffsN, pseries_diffs_inv_fact, pseries_diffs_sumE, pseries_diffs_equiv, is_cvg_pseries_diffs_equiv, pseries_snd_diffs
  • lemmas expR0, expR_ge1Dx, exp_coeffE, expRE
  • instance is_derive_expR
  • lemmas derivable_expR, continuous_expR, expRxDyMexpx, expRxMexpNx_1
  • lemmas pexpR_gt1, expR_gt0, expRN, expRD, expRMm
  • lemmas expR_gt1, expR_lt1, expRB, ltr_expR, ler_expR, expR_inj, expR_total_gt1, expR_total
  • definition ln
  • fact ln0
  • lemmas expK, lnK, ln1, lnM, ln_inj, lnV, ln_div, ltr_ln, ler_ln, lnX
  • lemmas le_ln1Dx, ln_sublinear, ln_ge0, ln_gt0
  • lemma continuous_ln
  • instance is_derive1_ln
  • definition exp_fun, notation `^
  • lemmas exp_fun_gt0, exp_funr1, exp_funr0, exp_fun1, ler_exp_fun, exp_funD, exp_fun_inv, exp_fun_mulrn
  • definition riemannR, lemmas riemannR_gt0, dvg_riemannR
• new file trigo.v
  • lemmas sqrtvR, eqr_div, big_nat_mul, cvg_series_cvg_series_group, lt_sum_lim_series
  • definitions periodic, alternating
  • lemmas periodicn, alternatingn
  • definition sin_coeff
  • lemmas sin_coeffE, sin_coeff_even, is_cvg_series_sin_coeff
  • definition sin
  • lemmas sinE
  • definition sin_coeff'
  • lemmas sin_coeff'E, cvg_sin_coeff', diffs_sin, series_sin_coeff0, sin0
  • definition cos_coeff
  • lemmas cos_ceff_2_0, cos_coeff_2_2, cos_coeff_2_4, cos_coeffE, is_cvg_series_cos_coeff
  • definition cos
  • lemma cosE
  • definition cos_coeff'
  • lemmas cos_coeff'E, cvg_cos_coeff', diffs_cos, series_cos_coeff0, cos0
  • instance is_derive_sin
  • lemmas derivable_sin, continuous_sin, is_derive_cos, derivable_cos, continuous_cos
  • lemmas cos2Dsin2, cos_max, cos_geN1, cos_le1, sin_max, sin_geN1, sin_le1
  • fact sinD_cosD
  • lemmas sinD, cosD
  • lemmas sin2cos2, cos2sin2, sin_mulr2n, cos_mulr2n
  • fact sinN_cosN
  • lemmas sinN, cosN
  • lemmas sin_sg, cos_sg, cosB, sinB
  • lemmas norm_cos_eq1, norm_sin_eq1, cos1sin0, sin0cos1, cos_norm
  • definition pi
  • lemmas pihalfE, cos2_lt0, cos_exists
  • lemmas sin2_gt0, cos_pihalf_uniq, pihalf_02_cos_pihalf, pihalf_02, pi_gt0, pi_ge0
  • lemmas sin_gt0_pihalf, cos_gt0_pihalf, cos_pihalf, sin_pihalf, cos_ge0_pihalf, cospi, sinpi
  • lemmas cos2pi, sin2pi, sinDpi, cosDpi, sinD2pi, cosD2pi
  • lemmas cosDpihalf, cosBpihalf, sinDpihalf, sinBpihalf, sin_ge0_pi
  • lemmas ltr_cos, ltr_sin, cos_inj, sin_inj
  • definition tan
  • lemmas tan0, tanpi, tanN, tanD, tan_mulr2n, cos2_tan2
  • lemmas tan_pihalf, tan_piquarter, tanDpi, continuous_tan
  • lemmas is_derive_tan, derivable_tan, ltr_tan, tan_inj
  • definition acos
  • lemmas acos_def, acos_ge0, acos_lepi, acosK, acos_gt0, acos_ltpi
  • lemmas cosK, sin_acos, continuous_acos, is_derive1_acos
  • definition asin
  • lemmas asin_def, asin_geNpi2, asin_lepi2, asinK, asin_ltpi2, asin_gtNpi2
  • lemmas sinK, cos_asin, continuous_asin, is_derive1_asin
  • definition atan
  • lemmas atan_def, atan_gtNpi2, atan_ltpi2, atanK, tanK
  • lemmas continuous_atan, cos_atan
  • instance is_derive1_atan

Changed

• in normedtype.v:
  • nbhs_minfty_lt renamed to nbhs_ninfty_lt_pos and changed to not use {posnum R}
  • nbhs_minfty_le renamed to nbhs_ninfty_le_pos and changed to not use {posnum R}
• in sequences.v:
  • lemma is_cvg_ereal_nneg_natsum: remove superfluous P parameter
  • statements of lemmas nondecreasing_cvg, nondecreasing_is_cvg, nonincreasing_cvg, nonincreasing_is_cvg use has_{l,u}bound predicates instead of requiring an additional variable
  • statement of lemma S1_sup use ubound instead of requiring an additional variable

Renamed

• in normedtype.v:
  • nbhs_minfty_lt_real -> nbhs_ninfty_lt
  • nbhs_minfty_le_real -> nbhs_ninfty_le
• in sequences.v:
  • cvgNminfty -> cvgNninfty
  • cvgPminfty -> cvgPninfty
  • ler_cvg_minfty -> ler_cvg_ninfty
  • nondecreasing_seq_ereal_cvg -> ereal_nondecreasing_cvg
• in normedtype.v:
  • nbhs_pinfty_gt -> nbhs_pinfty_gt_pos
  • nbhs_pinfty_ge -> nbhs_pinfty_ge_pos
  • nbhs_pinfty_gt_real -> nbhs_pinfty_gt
  • nbhs_pinfty_ge_real -> nbhs_pinfty_ge
• in measure.v:
  • measure_bigcup -> measure_bigsetU
• in ereal.v:
  • mulrEDr -> muleDr
  • mulrEDl -> muleDl
  • dmulrEDr -> dmuleDr
  • dmulrEDl -> dmuleDl
  • NEFin -> EFinN
  • addEFin -> EFinD
  • mulEFun -> EFinM
  • daddEFin -> dEFinD
  • dsubEFin -> dEFinB

Removed

• in ereal.v:
  • lemma subEFin

Infrastructure

• in Makefile.common
  • add doc and doc-clean targets

[0.3.11] - 2021-11-14

Added

• in boolp.v:
  • lemmas orA, andA
• in classical_sets.v
  • lemma setC_inj,
  • lemma setD1K,
  • lemma subTset,
  • lemma setUidPr, setUidl and setUidr,
  • lemma setIidPr, setIidl and setIidr,
  • lemma set_fset0, set_fset1, set_fsetI, set_fsetU,
  • lemma bigcap_inf, subset_bigcup_r, subset_bigcap_r, eq_bigcupl, eq_bigcapl, eq_bigcup, eq_bigcap, bigcupU, bigcapI, bigcup_const, bigcap_const, bigcapIr, bigcupUr, bigcap_set0, bigcap_set1, bigcap0, bigcapT, bigcupT, bigcapTP, setI_bigcupl, setU_bigcapl, bigcup_mkcond, bigcap_mkcond, setC_bigsetU, setC_bigsetI, bigcap_set_cond, bigcap_set, bigcap_split, bigcap_mkord, subset_bigsetI, subset_bigsetI_cond, bigcap_image
  • lemmas bigcup_setU1, bigcap_setU1, bigcup_setU, bigcap_setU, bigcup_fset, bigcap_fset, bigcup_fsetU1, bigcap_fsetU1, bigcup_fsetD1, bigcap_fsetD1,
  • definition mem_set : A u -> u \in A
  • lemmas in_setP and in_set2P
  • lemma forall_sig
  • definition patch, notation restrict and f \_ D, definitions restrict_dep and extend_dep, with lemmas restrict_depE, fun_eq_inP, extend_restrict_dep, extend_depK, restrict_extend_dep, restrict_dep_restrict, restrict_dep_setT
  • lemmas setUS, setSU, setUSS, setUCA, setUAC, setUACA, setUUl, setUUr
  • lemmas bigcup_image, bigcup_of_set1, set_fset0, set_fset1, set_fsetI, set_fsetU, set_fsetU1, set_fsetD, set_fsetD1,
  • notation [set` i]
  • notations set_itv, `[a, b], `]a, b], `[a, b[, `]a, b[, `]-oo, b], `]-oo, b[, `[a, +oo], `]a, +oo], `]-oo, +oo[
  • lemmas setDDl, setDDr
• in topology.v:
  • lemma fmap_comp
  • definition finSubCover
  • notations {uniform` A -> V } and {uniform U -> V} and their canonical structures of uniform type.
  • definition uniform_fun to cast into
  • notations {uniform A, F --> f } and {uniform, F --> f}
  • lemma uniform_cvgE
  • lemma uniform_nbhs
  • notation {ptws U -> V} and its canonical structure of topological type,
  • definition ptws_fun
  • notation {ptws F --> f }
  • lemma ptws_cvgE
  • lemma ptws_uniform_cvg
  • lemma cvg_restrict_dep
  • lemma eq_in_close
  • lemma hausdorrf_close_eq_in
  • lemma uniform_subset_nbhs
  • lemma uniform_subset_cvg
  • lemma uniform_restrict_cvg
  • lemma cvg_uniformU
  • lemma cvg_uniform_set0
  • notation {family fam, U -> V} and its canonical structure of topological type
  • notation {family fam, F --> f}
  • lemma fam_cvgP
  • lemma fam_cvgE
  • definition compactly_in
  • lemma family_cvg_subset
  • lemma family_cvg_finite_covers
  • lemma compact_cvg_within_compact
  • lemma le_bigmax
  • definition monotonous
  • lemma and_prop_in
  • lemmas mem_inc_segment, mem_dec_segment
  • lemmas ltr_distlC, ler_distlC
  • lemmas subset_ball_prop_in_itv, subset_ball_prop_in_itvcc
  • lemma dense_rat
• in normedtype.v:
  • lemma is_intervalPlt
  • lemma mule_continuous
  • lemmas ereal_is_cvgN, ereal_cvgZr, ereal_is_cvgZr, ereal_cvgZl, ereal_is_cvgZl, ereal_limZr, ereal_limZl, ereal_limN
  • lemma bound_itvE
  • lemmas nearN, near_in_itv
  • lemmas itvxx, itvxxP, subset_itv_oo_cc
  • lemma at_right_in_segment
  • notations f @`[a, b], g @`]a , b[
  • lemmas mono_mem_image_segment, mono_mem_image_itvoo, mono_surj_image_segment, inc_segment_image, dec_segment_image, inc_surj_image_segment, dec_surj_image_segment, inc_surj_image_segmentP, dec_surj_image_segmentP, mono_surj_image_segmentP
• in reals.v:
  • lemmas floor1, floor_neq0
  • lemma int_lbound_has_minimum
  • lemma rat_in_itvoo
• in ereal.v:
  • notation x +? y for adde_def x y
  • lemmas ge0_adde_def, onee_neq0, mule0, mul0e
  • lemmas mulrEDr, mulrEDl, ge0_muleDr, ge0_muleDl
  • lemmas ge0_sume_distrl, ge0_sume_distrr
  • lemmas mulEFin, mule_neq0, mule_ge0, muleA
  • lemma muleE
  • lemmas muleN, mulNe, muleNN, gee_pmull, lee_mul01Pr
  • lemmas lte_pdivr_mull, lte_pdivr_mulr, lte_pdivl_mull, lte_pdivl_mulr, lte_ndivl_mulr, lte_ndivl_mull, lte_ndivr_mull, lte_ndivr_mulr
  • lemmas lee_pdivr_mull, lee_pdivr_mulr, lee_pdivl_mull, lee_pdivl_mulr, lee_ndivl_mulr, lee_ndivl_mull, lee_ndivr_mull, lee_ndivr_mulr
  • lemmas mulrpinfty, mulrninfty, mulpinftyr, mulninftyr, mule_gt0
  • definition mulrinfty
  • lemmas mulN1e, muleN1
  • lemmas mule_ninfty_pinfty, mule_pinfty_ninfty, mule_pinfty_pinfty
  • lemmas mule_le0_ge0, mule_ge0_le0, pmule_rle0, pmule_lle0, nmule_lle0, nmule_rle0
  • lemma sube0
  • lemmas adde_le0, sume_le0, oppe_ge0, oppe_le0, lte_opp, gee_addl, gee_addr, lte_addr, gte_subl, gte_subr, lte_le_sub, lee_sum_npos_subset, lee_sum_npos, lee_sum_npos_ord, lee_sum_npos_natr, lee_sum_npos_natl, lee_sum_npos_subfset, lee_opp, le0_muleDl, le0_muleDr, le0_sume_distrl, le0_sume_distrr, adde_defNN, minEFin, mine_ninftyl, mine_ninftyr, mine_pinftyl, mine_pinftyr, oppe_max, oppe_min, mineMr, mineMl
  • definitions dual_adde
  • notations for the above in scope ereal_dual_scope delimited by dE
  • lemmas dual_addeE, dual_sumeE, dual_addeE_def, daddEFin, dsumEFin, dsubEFin, dadde0, dadd0e, daddeC, daddeA, daddeAC, daddeCA, daddeACA, doppeD, dsube0, dsub0e, daddeK, dfin_numD, dfineD, dsubeK, dsube_eq, dsubee, dadde_eq_pinfty, daddooe, dadde_Neq_pinfty, dadde_Neq_ninfty, desum_fset_pinfty, desum_pinfty, desum_fset_ninfty, desum_ninfty, dadde_ge0, dadde_le0, dsume_ge0, dsume_le0, dsube_lt0, dsubre_le0, dsuber_le0, dsube_ge0, lte_dadd, lee_daddl, lee_daddr, gee_daddl, gee_daddr, lte_daddl, lte_daddr, gte_dsubl, gte_dsubr, lte_dadd2lE, lee_dadd2l, lee_dadd2lE, lee_dadd2r, lee_dadd, lte_le_dadd, lee_dsub, lte_le_dsub, lee_dsum, lee_dsum_nneg_subset, lee_dsum_npos_subset, lee_dsum_nneg, lee_dsum_npos, lee_dsum_nneg_ord, lee_dsum_npos_ord, lee_dsum_nneg_natr, lee_dsum_npos_natr, lee_dsum_nneg_natl, lee_dsum_npos_natl, lee_dsum_nneg_subfset, lee_dsum_npos_subfset, lte_dsubl_addr, lte_dsubl_addl, lte_dsubr_addr, lee_dsubr_addr, lee_dsubl_addr, ge0_dsume_distrl, dmulrEDr, dmulrEDl, dge0_mulreDr, dge0_mulreDl, dle0_mulreDr, dle0_mulreDl, ge0_dsume_distrr, le0_dsume_distrl, le0_dsume_distrr, lee_abs_dadd, lee_abs_dsum, lee_abs_dsub, dadde_minl, dadde_minr, lee_dadde, lte_spdaddr
  • lemmas abse0, abse_ge0, lee_abs, abse_id, lee_abs_add, lee_abs_sum, lee_abs_sub, gee0_abs, gte0_abs, lee_abs, lte0_abs, abseM, lte_absl, eqe_absl
  • notations maxe, mine
  • lemmas maxEFin, adde_maxl, adde_maxr, maxe_pinftyl, maxe_pinftyr, maxe_ninftyl, maxe_ninftyr
  • lemmas sub0e, lee_wpmul2r, mule_ninfty_ninfty
  • lemmas sube_eq lte_pmul2r, lte_pmul2l, lte_nmul2l, lte_nmul2r, mule_le0, pmule_llt0, pmule_rlt0, nmule_llt0, nmule_rlt0, mule_lt0
  • lemmas maxeMl, maxeMr
  • lemmas lte_0_pinfty, lte_ninfty_0, lee_0_pinfty, lee_ninfty_0, oppe_gt0, oppe_lt0
  • lemma telescope_sume
  • lemmas lte_add_pinfty, lte_sum_pinfty
• in cardinality.v:
  • definition nat_of_pair, lemma nat_of_pair_inj
  • lemmas surjectiveE, surj_image_eq, can_surjective
• in sequences.v:
  • lemmas lt_lim, nondecreasing_dvg_lt, ereal_lim_sum
  • lemmas ereal_nondecreasing_opp, ereal_nondecreasing_is_cvg, ereal_nonincreasing_cvg, ereal_nonincreasing_is_cvg
• file realfun.v:
  • lemmas itv_continuous_inj_le, itv_continuous_inj_ge, itv_continuous_inj_mono
  • lemmas segment_continuous_inj_le, segment_continuous_inj_ge, segment_can_le, segment_can_ge, segment_can_mono
  • lemmas segment_continuous_surjective, segment_continuous_le_surjective, segment_continuous_ge_surjective
  • lemmas continuous_inj_image_segment, continuous_inj_image_segmentP, segment_continuous_can_sym, segment_continuous_le_can_sym, segment_continuous_ge_can_sym, segment_inc_surj_continuous, segment_dec_surj_continuous, segment_mono_surj_continuous
  • lemmas segment_can_le_continuous, segment_can_ge_continuous, segment_can_continuous
  • lemmas near_can_continuousAcan_sym, near_can_continuous, near_continuous_can_sym
  • lemmas exp_continuous, sqr_continuous, sqrt_continuous.
• in measure.v:
  • definition seqDU
  • lemmas trivIset_seqDU, bigsetU_seqDU, seqDU_bigcup_eq, seqDUE
  • lemmas bigcup_measurable, bigcap_measurable, bigsetI_measurable

Changed

• in classical_sets.v
  • setU_bigcup -> bigcupUl and reversed
  • setI_bigcap -> bigcapIl and reversed
  • removed spurious disjunction in bigcup0P
  • bigcup_ord -> bigcup_mkord and reversed
  • bigcup_of_set1 -> bigcup_imset1
  • bigcupD1 -> bigcup_setD1 and bigcapD1 -> bigcap_setD1 and rephrased using P `\ x instead of P `&` ~` [set x]
  • order of arguments for setIS, setSI, setUS, setSU, setSD, setDS
  • generalize lemma perm_eq_trivIset
• in topology.v:
  • replace closed_cvg_loc and closed_cvg by a more general lemma closed_cvg
• in normedtype.v:
  • remove useless parameter from lemma near_infty_natSinv_lt
  • definition is_interval
  • the following lemmas have been generalized to orderType, renamed as follows, moved out of the module BigmaxBigminr to topology.v:
    • bigmaxr_mkcond -> bigmax_mkcond
    • bigmaxr_split -> bigmax_split
    • bigmaxr_idl -> bigmax_idl
    • bigmaxrID -> bigmaxID
    • bigmaxr_seq1 -> bigmax_seq1
    • bigmaxr_pred1_eq -> bigmax_pred1_eq
    • bigmaxr_pred1 -> bigmax_pred1
    • bigmaxrD1 -> bigmaxD1
    • ler_bigmaxr_cond -> ler_bigmax_cond
    • ler_bigmaxr -> ler_bigmax
    • bigmaxr_lerP -> bigmax_lerP
    • bigmaxr_sup -> bigmax_sup
    • bigmaxr_ltrP -> bigmax_ltrP
    • bigmaxr_gerP -> bigmax_gerP
    • bigmaxr_eq_arg -> bigmax_eq_arg
    • bigmaxr_gtrP -> bigmax_gtrP
    • eq_bigmaxr -> eq_bigmax
    • module BigmaxBigminr -> Bigminr
• in ereal.v:
  • change definition mule such that 0 x oo = 0
  • adde now defined using nosimpl and adde_subdef
  • mule now defined using nosimpl and mule_subdef
  • lemmas lte_addl, lte_subl_addr, lte_subl_addl, lte_subr_addr, lte_subr_addr, lte_subr_addr, lb_ereal_inf_adherent
  • oppeD to use fin_num
  • weaken realDomainType to numDomainType in mule_ninfty_pinfty, mule_pinfty_ninfty, mule_pinfty_pinfty, mule_ninfty_ninfty, mule_neq0, mule_ge0, mule_le0, mule_gt0, mule_le0_ge0, mule_ge0_le0
• in reals.v:
  • generalize from realType to realDomainType lemmas has_ub_image_norm, has_inf_supN
• in sequences.v:
  • generalize from realType to realFieldType lemmas cvg_has_ub, cvg_has_sup, cvg_has_inf
  • change the statements of cvgPpinfty, cvgPminfty, cvgPpinfty_lt
  • generalize nondecreasing_seqP, nonincreasing_seqP, increasing_seqP, decreasing_seqP to equivalences
  • generalize lee_lim, ereal_cvgD_pinfty_fin, ereal_cvgD_ninfty_fin, ereal_cvgD, ereal_limD, ereal_pseries0, eq_ereal_pseries from realType to realFieldType
  • lemma ereal_pseries_pred0 moved from csum.v, minor generalization
• in landau.v:
  • lemma cvg_shift renamed to cvg_comp_shift and moved to normedtype.v
• in measure.v:
  • lemmas measureDI, measureD, sigma_finiteP
• exist_congr -> eq_exist and moved from classsical_sets.v to boolp.v
• predeqP moved from classsical_sets.v to boolp.v
• moved from landau.v to normedtype.v:
  • lemmas comp_shiftK, comp_centerK, shift0, center0, near_shift, cvg_shift
• lemma exists2P moved from topology.v to boolp.v
• move from sequences.v to normedtype.v and generalize from nat to T : topologicalType
  • lemmas ereal_cvgN

Renamed

• in classical_sets.v
  • eqbigcup_r -> eq_bigcupr
  • eqbigcap_r -> eq_bigcapr
  • bigcup_distrr -> setI_bigcupr
  • bigcup_distrl -> setI_bigcupl
  • bigcup_refl -> bigcup_splitn
  • setMT -> setMTT
• in ereal.v:
  • adde -> adde_subdef
  • mule -> mule_subdef
  • real_of_extended -> fine
  • real_of_extendedN -> fineN
  • real_of_extendedD -> fineD
  • EFin_real_of_extended -> fineK
  • real_of_extended_expand -> fine_expand
• in sequences.v:
  • nondecreasing_seq_ereal_cvg -> nondecreasing_ereal_cvg
• in topology.v:
  • nbhs' -> dnbhs
  • nbhsE' -> dnbhs
  • nbhs'_filter -> dnbhs_filter
  • nbhs'_filter_on -> dnbhs_filter_on
  • nbhs_nbhs' -> nbhs_dnbhs
  • Proper_nbhs'_regular_numFieldType -> Proper_dnbhs_regular_numFieldType
  • Proper_nbhs'_numFieldType -> Proper_dnbhs_numFieldType
  • ereal_nbhs' -> ereal_dnbhs
  • ereal_nbhs'_filter -> ereal_dnbhs_filter
  • ereal_nbhs'_le -> ereal_dnbhs_le
  • ereal_nbhs'_le_finite -> ereal_dnbhs_le_finite
  • Proper_nbhs'_numFieldType -> Proper_dnbhs_numFieldType
  • Proper_nbhs'_realType -> Proper_dnbhs_realType
  • nbhs'0_lt -> dnbhs0_lt
  • nbhs'0_le -> dnbhs0_le
  • continuity_pt_nbhs' -> continuity_pt_dnbhs
• in measure.v:
  • measure_additive2 -> measureU
  • measure_additive -> measure_bigcup

Removed

• in boolp.v:
  • definition PredType
  • local notation predOfType
• in nngnum.v:
  • module BigmaxrNonneg containing the following lemmas:
    • bigmaxr_mkcond, bigmaxr_split, bigmaxr_idl, bigmaxrID, bigmaxr_seq1, bigmaxr_pred1_eq, bigmaxr_pred1, bigmaxrD1, ler_bigmaxr_cond, ler_bigmaxr, bigmaxr_lerP, bigmaxr_sup, bigmaxr_ltrP, bigmaxr_gerP, bigmaxr_gtrP
• in sequences.v:
  • lemma closed_seq
• in normedtype.v:
  • lemma is_intervalPle
• in topology.v:
  • lemma continuous_cst
  • definition cvg_to_locally
• in csum.v:
  • lemma ub_ereal_sup_adherent_img

[0.3.10] - 2021-08-11

Added

• in classical_sets.v:
  • lemmas bigcup_image, bigcup_of_set1
  • lemmas bigcupD1, bigcapD1
• in boolp.v:
  • definitions equality_mixin_of_Type, choice_of_Type
• in normedtype.v:
  • lemma cvg_bounded_real
  • lemma pseudoMetricNormedZModType_hausdorff
• in sequences.v:
  • lemmas seriesN, seriesD, seriesZ, is_cvg_seriesN, lim_seriesN, is_cvg_seriesZ, lim_seriesZ, is_cvg_seriesD, lim_seriesD, is_cvg_seriesB, lim_seriesB, lim_series_le, lim_series_norm
• in measure.v:
  • HB.mixin AlgebraOfSets_from_RingOfSets
  • HB.structure AlgebraOfSets and notation algebraOfSetsType
  • HB.instance T_isAlgebraOfSets in HB.builders isAlgebraOfSets
  • lemma bigcup_set_cond
  • definition measurable_fun
  • lemma adde_undef_nneg_series
  • lemma adde_def_nneg_series
  • lemmas cvg_geometric_series_half, epsilon_trick
  • definition measurable_cover
  • lemmas cover_measurable, cover_subset
  • definition mu_ext
  • lemmas le_mu_ext, mu_ext_ge0, mu_ext0, measurable_uncurry, mu_ext_sigma_subadditive
  • canonical outer_measure_of_measure

Changed

• in ereal.v, definition adde_undef changed to adde_def
  • consequently, the following lemmas changed:
    • in ereal.v, adde_undefC renamed to adde_defC, fin_num_adde_undef renamed to fin_num_adde_def
    • in sequences.v, ereal_cvgD and ereal_limD now use hypotheses with adde_def
• in sequences.v:
  • generalize {in,de}creasing_seqP, non{in,de}creasing_seqP from numDomainType to porderType
• in normedtype.v:
  • generalized from normedModType to pseudoMetricNormedZmodType:
    • nbhs_le_nbhs_norm
    • nbhs_norm_le_nbhs
    • nbhs_nbhs_norm
    • nbhs_normP
    • filter_from_norm_nbhs
    • nbhs_normE
    • filter_from_normE
    • near_nbhs_norm
    • nbhs_norm_ball_norm
    • nbhs_ball_norm
    • ball_norm_dec
    • ball_norm_sym
    • ball_norm_le
    • cvg_distP
    • cvg_dist
    • nbhs_norm_ball
    • dominated_by
    • strictly_dominated_by
    • sub_dominatedl
    • sub_dominatedr
    • dominated_by1
    • strictly_dominated_by1
    • ex_dom_bound
    • ex_strict_dom_bound
    • bounded_near
    • boundedE
    • sub_boundedr
    • sub_boundedl
    • ex_bound
    • ex_strict_bound
    • ex_strict_bound_gt0
    • norm_hausdorff
    • norm_closeE
    • norm_close_eq
    • norm_cvg_unique
    • norm_cvg_eq
    • norm_lim_id
    • norm_cvg_lim
    • norm_lim_near_cst
    • norm_lim_cst
    • norm_cvgi_unique
    • norm_cvgi_map_lim
    • distm_lt_split
    • distm_lt_splitr
    • distm_lt_splitl
    • normm_leW
    • normm_lt_split
    • cvg_distW
    • continuous_cvg_dist
    • add_continuous
• in measure.v:
  • generalize lemma eq_bigcupB_of
  • HB.mixin Measurable_from_ringOfSets changed to Measurable_from_algebraOfSets
  • HB.instance T_isRingOfSets becomes T_isAlgebraOfSets in HB.builders isMeasurable
  • lemma measurableC now applies to algebraOfSetsType instead of measureableType
• moved from normedtype.v to reals.v:
  • lemmas inf_lb_strict, sup_ub_strict
• moved from sequences.v to reals.v:
  • lemma has_ub_image_norm

Renamed

• in classical_sets.v:
  • bigcup_mkset -> bigcup_set
  • bigsetU -> bigcup
  • bigsetI -> bigcap
  • trivIset_bigUI -> trivIset_bigsetUI
• in measure.v:
  • isRingOfSets -> isAlgebraOfSets
  • B_of -> seqD
  • trivIset_B_of -> trivIset_seqD
  • UB_of -> setU_seqD
  • bigUB_of -> bigsetU_seqD
  • eq_bigsetUB_of -> eq_bigsetU_seqD
  • eq_bigcupB_of -> eq_bigcup_seqD
  • eq_bigcupB_of_bigsetU -> eq_bigcup_seqD_bigsetU

Removed

• in nngnum.v:
  • lemma filter_andb

[0.3.9] - 2021-06-12

Added

• in sequences.v:
  • lemma dvg_harmonic
• in classical_sets.v:
  • definitions image, image2

Changed

• in classical_sets.v
  • notations [set E | x in A] and [set E | x in A & y in B] now use definitions image and image2 resp.
  • notation f @` A now uses the definition image
  • the order of arguments of image has changed compared to version 0.3.7: it is now image A f (it used to be image f A)

Removed

• in sequences.v:
  • lemma iter_addr

[0.3.8] - 2021-06-01

Added

• file reals.v:
  • lemmas le_floor, le_ceil
• in ereal.v:
  • lemmas big_nat_widenl, big_geq_mkord
  • lemmas lee_sum_nneg_natr, lee_sum_nneg_natl
  • lemmas ereal_sup_gt, ereal_inf_lt
  • notation 0/1 for 0%R%:E/1%R:%E in ereal_scope
• in classical_sets.v
  • lemma subset_bigsetU_cond
  • lemma eq_imagel
• in sequences.v:
  • notations \sum_(i <oo) F i
  • lemmas ereal_pseries_sum_nat, lte_lim
  • lemmas is_cvg_ereal_nneg_natsum_cond, is_cvg_ereal_nneg_natsum
  • lemma ereal_pseriesD, ereal_pseries0, eq_ereal_pseries
  • lemmas leq_fact, prod_rev, fact_split
  • definition exp_coeff
  • lemmas exp_coeff_ge0, series_exp_coeff0, is_cvg_series_exp_coeff_pos, normed_series_exp_coeff, is_cvg_series_exp_coeff , cvg_exp_coeff
  • definition expR
• in measure.v:
  • lemma eq_bigcupB_of_bigsetU
  • definitions caratheodory_type
  • definition caratheodory_measure and lemma caratheodory_measure_complete
  • internal definitions and lemmas that may be deprecated and hidden in the future:
    • caratheodory_measurable, notation ... .-measurable,
    • le_caratheodory_measurable, outer_measure_bigcup_lim, caratheodory_measurable_{set0,setC,setU_le,setU,bigsetU,setI,setD} disjoint_caratheodoryIU, caratheodory_additive, caratheodory_lim_lee, caratheodory_measurable_trivIset_bigcup, caratheodory_measurable_bigcup
  • definition measure_is_complete
• file csum.v:
  • lemmas ereal_pseries_pred0, ub_ereal_sup_adherent_img
  • definition fsets, lemmas fsets_set0, fsets_self, fsetsP, fsets_img
  • definition fsets_ord, lemmas fsets_ord_nat, fsets_ord_subset
  • definition csum, lemmas csum0, csumE, csum_ge0, csum_fset csum_image, ereal_pseries_csum, csum_bigcup
  • notation \csum_(i in S) a i
• file cardinality.v
  • lemmas in_inj_comp, enum0, enum_recr, eq_set0_nil, eq_set0_fset0, image_nat_maximum, fset_nat_maximum
  • defintion surjective, lemmas surjective_id, surjective_set0, surjective_image, surjective_image_eq0, surjective_comp
  • definition set_bijective,
  • lemmas inj_of_bij, sur_of_bij, set_bijective1, set_bijective_image, set_bijective_subset, set_bijective_comp
  • definition inverse
  • lemmas injective_left_inverse, injective_right_inverse, surjective_right_inverse,
  • notation `I_n
  • lemmas II0, II1, IIn_eq0, II_recr
  • lemmas set_bijective_D1, pigeonhole, Cantor_Bernstein
  • definition card_le, notation _ #<= _
  • lemmas card_le_surj, surj_card_le, card_lexx, card_le0x, card_le_trans, card_le0P, card_le_II
  • definition card_eq, notation _ #= _
  • lemmas card_eq_sym, card_eq_trans, card_eq00, card_eqP, card_eqTT, card_eq_II, card_eq_le, card_eq_ge, card_leP
  • lemma set_bijective_inverse
  • definition countable
  • lemmas countable0, countable_injective, countable_trans
  • definition set_finite
  • lemmas set_finiteP, set_finite_seq, set_finite_countable, set_finite0
  • lemma set_finite_bijective
  • lemmas subset_set_finite, subset_card_le
  • lemmas injective_set_finite, injective_card_le, set_finite_preimage
  • lemmas surjective_set_finite, surjective_card_le
  • lemmas set_finite_diff, card_le_diff
  • lemmas set_finite_inter_set0_union, set_finite_inter
  • lemmas ex_in_D, definitions min_of_D, min_of_D_seq, infsub_enum, lemmas min_of_D_seqE, increasing_infsub_enum, sorted_infsub_enum, injective_infsub_enum, subset_infsub_enum, infinite_nat_subset_countable
  • definition enumeration, lemmas enumeration_id, enumeration_set0.
  • lemma ex_enum_notin, definitions min_of, minf_of_e_seq, smallest_of
  • definition enum_wo_rep, lemmas enum_wo_repE, min_of_e_seqE, smallest_of_e_notin_enum_wo_rep, injective_enum_wo_rep, surjective_enum_wo_rep, set_bijective_enum_wo_rep, enumration_enum_wo_rep, countable_enumeration
  • lemmas infinite_nat, infinite_prod_nat, countable_prod_nat, countably_infinite_prod_nat

Changed

• in classical_sets.v
  • lemma subset_bigsetU
  • notation f @` A defined as [set f x | x in A] instead of using image
• in ereal.v:
  • change implicits of lemma lee_sum_nneg_ord
  • ereal_sup_ninfty and ereal_inf_pinfty made equivalences
  • change the notation {ereal R} to \bar R and attach it to the scope ereal_scope
  • argument of %:E in %R by default
  • F argument of \sum in %E by default
• in topology.v:
  • change implicits of lemma cvg_app
• in normedtype.v:
  • coord_continuous generalized
• in sequences.v:
  • change implicits of lemma is_cvg_ereal_nneg_series
  • statements changed from using sum of ordinals to sum of nats
    • definition series
    • lemmas ereal_nondecreasing_series, ereal_nneg_series_lim_ge
    • lemmas is_cvg_ereal_nneg_series_cond, is_cvg_ereal_nneg_series
    • lemmas ereal_nneg_series_lim_ge0, ereal_nneg_series_pinfty

Renamed

• in ereal.v:
  • er -> extended
  • ERFin -> EFin
  • ERPInf -> EPInf
  • ERNInf -> ENInf
  • real_of_er -> real_of_extended
  • real_of_erD -> real_of_extendedD
  • ERFin_real_of_er -> EFin_real_of_extended
  • real_of_er_expand -> real_of_extended_expand
  • NERFin -> NEFin
  • addERFin -> addEFin
  • sumERFin-> sumEFin
  • subERFin -> subEFin
• in reals.v:
  • ler_ceil -> ceil_ge
  • Rceil_le -> le_Rceil
  • le_Rceil -> Rceil_ge
  • ge_Rfloor -> Rfloor_le
  • ler_floor -> floor_le
  • Rfloor_le -> le_Rfloor
• in topology.v:
  • lemmas onT_can -> onS_can, onT_can_in -> onS_can_in, in_onT_can -> ``in_onS_can` (now in MathComp)
• in sequences,v:
  • is_cvg_ereal_nneg_series_cond
• in forms.v:
  • symmetric -> symmetric_form

Removed

• in classical_sets.v
  • lemmas eq_set_inl, set_in_in
  • definition image
• from topology.v:
  • lemmas homoRL_in, homoLR_in, homo_mono_in, monoLR_in, monoRL_in, can_mono_in, onW_can, onW_can_in, in_onW_can, onT_can, onT_can_in, in_onT_can (now in MathComp)
• in forms.v:
  • lemma mxdirect_delta, row_mx_eq0, col_mx_eq0, map_mx_comp

[0.3.7] - 2021-04-01

Added

• in topology.v:
  • global instance ball_filter
  • module regular_topology with an Exports submodule
    • canonicals pointedType, filteredType, topologicalType, uniformType, pseudoMetricType
  • module numFieldTopology with an Exports submodule
    • many canonicals and coercions
  • global instance Proper_nbhs'_regular_numFieldType
  • definition dense and lemma denseNE
• in normedtype.v:
  • definitions ball_, pointed_of_zmodule, filtered_of_normedZmod
  • lemmas ball_norm_center, ball_norm_symmetric, ball_norm_triangle
  • definition pseudoMetric_of_normedDomain
  • lemma nbhs_ball_normE
  • global instances Proper_nbhs'_numFieldType, Proper_nbhs'_realType
  • module regular_topology with an Exports submodule
    • canonicals pseudoMetricNormedZmodType, normedModType.
  • module numFieldNormedType with an Exports submodule
    • many canonicals and coercions
    • exports Export numFieldTopology.Exports
  • canonical R_regular_completeType, R_regular_CompleteNormedModule
• in reals.v:
  • lemmas Rfloor_lt0, floor_lt0, ler_floor, ceil_gt0, ler_ceil
  • lemmas has_sup1, has_inf1
• in ereal.v:
  • lemmas ereal_ballN, le_ereal_ball, ereal_ball_ninfty_oversize, contract_ereal_ball_pinfty, expand_ereal_ball_pinfty, contract_ereal_ball_fin_le, contract_ereal_ball_fin_lt, expand_ereal_ball_fin_lt, ball_ereal_ball_fin_lt, ball_ereal_ball_fin_le, sumERFin, ereal_inf1, eqe_oppP, eqe_oppLRP, oppe_subset, ereal_inf_pinfty
  • definition er_map
  • definition er_map
  • lemmas adde_undefC, real_of_erD, fin_num_add_undef, addeK, subeK, subee, sube_le0, lee_sub
  • lemmas addeACA, muleC, mule1, mul1e, abseN
  • enable notation x \is a fin_num
    • definition fin_num, fact fin_num_key, lemmas fin_numE, fin_numP
• in classical_sets.v:
  • notation [disjoint ... & ..]
  • lemmas mkset_nil, bigcup_mkset, bigcup_nonempty, bigcup0, bigcup0P, subset_bigcup_r, eqbigcup_r, eq_set_inl, set_in_in
• in nngnum.v:
  • instance invr_nngnum
• in posnum.v:
  • instance posnum_nngnum

Changed

• in ereal.v:

  • generalize lemma lee_sum_nneg_subfset
  • lemmas nbhs_oo_up_e1, nbhs_oo_down_e1, nbhs_oo_up_1e, nbhs_oo_down_1e nbhs_fin_out_above, nbhs_fin_out_below, nbhs_fin_out_above_below nbhs_fin_inbound

• in sequences.v:

  • generalize lemmas ereal_nondecreasing_series, is_cvg_ereal_nneg_series, ereal_nneg_series_lim_ge0, ereal_nneg_series_pinfty

• in measure.v:

  • generalize lemma bigUB_of
  • generalize theorem Boole_inequality

• in classical_sets.v:

  • change the order of arguments of subset_trans

• canonicals and coercions have been changed so that there is not need anymore for explicit types casts to R^o, [filteredType R^o of R^o], [filteredType R^o * R^o of R^o * R^o], [lmodType R of R^o], [normedModType R of R^o],[topologicalType of R^o], [pseudoMetricType R of R^o]

• sequences.v now imports numFieldNormedType.Exports

• topology.v now imports reals

• normedtype.v now imports vector, fieldext, falgebra, numFieldTopology.Exports

• derive.v now imports numFieldNormedType.Exports

Renamed

• in ereal.v:
  • is_realN -> fin_numN
  • is_realD -> fin_numD
  • ereal_sup_set0 -> ereal_sup0
  • ereal_sup_set1 -> ereal_sup1
  • ereal_inf_set0 -> ereal_inf0

Removed

• in topology.v:
  • section numFieldType_canonical
• in normedtype.v:
  • lemma R_ball
  • definition numFieldType_pseudoMetricNormedZmodMixin
  • canonical numFieldType_pseudoMetricNormedZmodType
  • global instance Proper_nbhs'_realType
  • lemma R_normZ
  • definition numFieldType_NormedModMixin
  • canonical numFieldType_normedModType
• in ereal.v:
  • definition is_real

[0.3.6] - 2021-03-04

Added

• in boolp.v:
  • lemmas iff_notr, iff_not2
• in classical_sets.v:
  • lemmas subset_has_lbound, subset_has_ubound
  • lemma mksetE
  • definitions cover, partition, pblock_index, pblock
  • lemmas trivIsetP, trivIset_sets, trivIset_restr, perm_eq_trivIset
  • lemma fdisjoint_cset
  • lemmas setDT, set0D, setD0
  • lemmas setC_bigcup, setC_bigcap
• in reals.v:
  • lemmas sup_setU, inf_setU
  • lemmas RtointN, floor_le0
  • definition Rceil, lemmas isint_Rceil, Rceil0, le_Rceil, Rceil_le, Rceil_ge0
  • definition ceil, lemmas RceilE, ceil_ge0, ceil_le0
• in ereal.v:
  • lemmas esum_fset_ninfty, esum_fset_pinfty, esum_pinfty
• in normedtype.v:
  • lemmas ereal_nbhs'_le, ereal_nbhs'_le_finite
  • lemmas ball_open
  • definition closed_ball_, lemmas closed_closed_ball_
  • definition closed_ball, lemmas closed_ballxx, closed_ballE, closed_ball_closed, closed_ball_subset, nbhs_closedballP, subset_closed_ball
  • lemmas nbhs0_lt, nbhs'0_lt, interior_closed_ballE, open_nbhs_closed_ball`
  • section "LinearContinuousBounded"
    • lemmas linear_boundedP, linear_continuous0, linear_bounded0, continuousfor0_continuous, linear_bounded_continuous, bounded_funP
• in measure.v:
  • definition sigma_finite

Changed

• in classical_sets.v:
  • generalization and change of trivIset (and thus lemmas trivIset_bigUI and trivIset_setI)
  • bigcup_distrr, bigcup_distrl generalized
• header in normedtype.v, precisions on bounded_fun
• in reals.v:
  • floor_ge0 generalized and renamed to floorR_ge_int
• in ereal.v, ereal_scope notation scope:
  • x <= y notation changed to lee (x : er _) (y : er _) and only printing notation x <= y for lee x y
  • same change for <
  • change extended to notations _ <= _ <= _, _ < _ <= _, _ <= _ < _, _ < _ < _

Renamed

• in reals.v:
  • floor -> Rfloor
  • isint_floor -> isint_Rfloor
  • floorE -> RfloorE
  • mem_rg1_floor -> mem_rg1_Rfloor
  • floor_ler -> Rfloor_ler
  • floorS_gtr -> RfloorS_gtr
  • floor_natz -> Rfloor_natz
  • Rfloor -> Rfloor0
  • floor1 -> Rfloor1
  • ler_floor -> ler_Rfloor
  • floor_le0 -> Rfloor_le0
  • ifloor -> floor
  • ifloor_ge0 -> floor_ge0
• in topology.v:
  • ball_ler -> le_ball
• in normedtype.v, bounded_on -> bounded_near
• in measure.v:
  • AdditiveMeasure.Measure -> AdditiveMeasure.Axioms
  • OuterMeasure.OuterMeasure -> OuterMeasure.Axioms

Removed

• in topology.v:
  • ball_le
• in classical_sets.v:
  • lemma bigcapCU
• in sequences.v:
  • lemmas ler_sum_nat, sumr_const_nat

[0.3.5] - 2020-12-21

Added

• in classical_sets.v:
  • lemmas predeqP, seteqP

Changed

• Requires:
  • MathComp >= 1.12
• in boolp.v:
  • lemmas contra_not, contra_notT, contra_notN, contra_not_neq, contraPnot are now provided by MathComp 1.12
• in normedtype.v:
  • lemmas ltr_distW, ler_distW are now provided by MathComp 1.12 as lemmas ltr_distlC_subl and ler_distl_subl
  • lemmas maxr_real and bigmaxr_real are now provided by MathComp 1.12 as lemmas max_real and bigmax_real
  • definitions isBOpen and isBClosed are replaced by the definition bound_side
  • definition Rhull now uses BSide instead of BOpen_if

Removed

• Drop support for MathComp 1.11
• in topology.v:
  • Typeclasses Opaque fmap.

[0.3.4] - 2020-12-12

Added

• in classical_sets.v:
  • lemma bigcup_distrl
  • definition trivIset
  • lemmas trivIset_bigUI, trivIset_setI
• in ereal.v:
  • definition mule and its notation * (scope ereal_scope)
  • definition abse and its notation `| | (scope ereal_scope)
• in normedtype.v:
  • lemmas closure_sup, near_infty_natSinv_lt, limit_pointP
  • lemmas closure_gt, closure_lt
  • definition is_interval, is_intervalPle, interval_is_interval
  • lemma connected_intervalP
  • lemmas interval_open and interval_closed
  • lemmas inf_lb_strict, sup_ub_strict, interval_unbounded_setT, right_bounded_interior, interval_left_unbounded_interior, left_bounded_interior, interval_right_unbounded_interior, interval_bounded_interior
  • definition Rhull
  • lemma sub_Rhull, is_intervalP
• in measure.v:
  • definition bigcup2, lemma bigcup2E
  • definitions isSemiRingOfSets, SemiRingOfSets, notation semiRingOfSetsType
  • definitions RingOfSets_from_semiRingOfSets, RingOfSets, notation ringOfSetsType
  • factory: isRingOfSets
  • definitions Measurable_from_ringOfSets, Measurable
  • lemma semiRingOfSets_measurable{I,D}
  • definition diff_fsets, lemmas semiRingOfSets_diff_fsetsE, semiRingOfSets_diff_fsets_disjoint
  • definitions isMeasurable
  • factory: isMeasurable
  • lemma bigsetU_measurable, measurable_bigcap
  • definitions semi_additive2, semi_additive, semi_sigma_additive
  • lemmas semi_additive2P, semi_additiveE, semi_additive2E, semi_sigma_additive_is_additive, semi_sigma_additiveE
  • Module AdditiveMeasure
    • notations additive_measure, {additive_measure set T -> {ereal R}}
  • lemmas measure_semi_additive2, measure_semi_additive, measure_semi_sigma_additive
  • lemma semi_sigma_additive_is_additive, canonical/coercion measure_additive_measure
  • lemma sigma_additive_is_additive
  • notations ringOfSetsType, outer_measure
  • definition negligible and its notation .-negligible
  • lemmas negligibleP, negligible_set0
  • definition almost_everywhere and its notation {ae mu, P}
  • lemma satisfied_almost_everywhere
  • definition sigma_subadditive
  • Module OuterMeasure
    • notation outer_measure, {outer_measure set T -> {ereal R}}
  • lemmas outer_measure0, outer_measure_ge0, le_outer_measure, outer_measure_sigma_subadditive, le_outer_measureIC
• in boolp.v:
  • lemmas and3_asboolP, or3_asboolP, not_and3P
• in classical_sets.v:
  • lemma bigcup_sup
• in topology.v:
  • lemmas closure0, separatedC, separated_disjoint, connectedP, connected_subset, bigcup_connected
  • definition connected_component
  • lemma component_connected

Changed

• in ereal.v:
  • notation x >= y defined as y <= x (only parsing) instead of gee
  • notation x > y defined as y < x (only parsing) instead of gte
  • definition mkset
  • lemma eq_set
• in classical_sets.v:
  • notation [set x : T | P] now use definition mkset
• in reals.v:
  • lemmas generalized from realType to numDomainType: setNK, memNE, lb_ubN, ub_lbN, nonemptyN, has_lb_ubN
  • lemmas generalized from realType to realDomainType: has_ubPn, has_lbPn

Renamed

• in classical_sets.v:
  • subset_empty -> subset_nonempty
• in measure.v:
  • sigma_additive_implies_additive -> sigma_additive_is_additive
• in topology.v:
  • nbhs_of -> locally_of
• in topology.v:
  • connect0 -> connected0

[0.3.3] - 2020-11-11

Added

• in boolp.v:
  • lemma not_andP
  • lemma not_exists2P
• in classical_sets.v:
  • lemmas setIIl, setIIr, setCS, setSD, setDS, setDSS, setCI, setDUr, setDUl, setIDA, setDD
  • definition dep_arrow_choiceType
  • lemma bigcup_set0
  • lemmas setUK, setKU, setIK, setKI, subsetEset, subEset, complEset, botEset, topEset, meetEset, joinEset, subsetPset, properPset
  • Canonical porderType, latticeType, distrLatticeType, blatticeType, tblatticeType, bDistrLatticeType, tbDistrLatticeType, cbDistrLatticeType, ctbDistrLatticeType
  • lemmas set0M, setM0, image_set0_set0, subset_set1, preimage_set0
  • lemmas setICr, setUidPl, subsets_disjoint, disjoints_subset, setDidPl, setIidPl, setIS, setSI, setISS, bigcup_recl, bigcup_distrr, setMT
  • new lemmas: lb_set1, ub_lb_set1, ub_lb_refl, lb_ub_lb
  • new definitions and lemmas: infimums, infimum, infimums_set1, is_subset1_infimum
  • new lemmas: ge_supremum_Nmem, le_infimum_Nmem, nat_supremums_neq0
  • lemmas setUCl, setDv
  • lemmas image_preimage_subset, image_subset, preimage_subset
  • definition proper and its notation <
  • lemmas setUK, setKU, setIK, setKI
  • lemmas setUK, setKU, setIK, setKI, subsetEset, subEset, complEset, botEset, topEset, meetEset, joinEset, properEneq
  • Canonical porderType, latticeType, distrLatticeType, blatticeType, tblatticeType, bDistrLatticeType, tbDistrLatticeType, cbDistrLatticeType, ctbDistrLatticeType on classical set.
• file nngnum.v
• in topology.v:
  • definition meets and its notation #
  • lemmas meetsC, meets_openr, meets_openl, meets_globallyl, meets_globallyr , meetsxx and proper_meetsxx.
  • definition limit_point
  • lemmas subset_limit_point, closure_limit_point, closure_subset, closureE, closureC, closure_id
  • lemmas cluster_nbhs, clusterEonbhs, closureEcluster
  • definition separated
  • lemmas connected0, connectedPn, connected_continuous_connected
  • lemmas closureEnbhs, closureEonbhs, limit_pointEnbhs, limit_pointEonbhs, closeEnbhs, closeEonbhs.
• in ereal.v:
  • notation \+ (ereal_scope) for function addition
  • notations > and >= for comparison of extended real numbers
  • definition is_real, lemmas is_realN, is_realD, ERFin_real_of_er
  • basic lemmas: addooe, adde_Neq_pinfty, adde_Neq_ninfty, addERFin, subERFin, real_of_erN, lb_ereal_inf_adherent
  • arithmetic lemmas: oppeD, subre_ge0, suber_ge0, lee_add2lE, lte_add2lE, lte_add, lte_addl, lte_le_add, lte_subl_addl, lee_subr_addr, lee_subl_addr, lte_spaddr
  • lemmas gee0P, sume_ge0, lee_sum_nneg, lee_sum_nneg_ord, lee_sum_nneg_subset, lee_sum_nneg_subfset
  • lemma lee_addr
  • lemma lee_adde
  • lemma oppe_continuous
  • lemmas ereal_nbhs_pinfty_ge, ereal_nbhs_ninfty_le
• in sequences.v:
  • definitions arithmetic, geometric, geometric_invn
  • lemmas increasing_series, cvg_shiftS, mulrn_arithmetic, exprn_geometric, cvg_arithmetic, cvg_expr, geometric_seriesE, cvg_geometric_series, is_cvg_geometric_series.
  • lemmas ereal_cvgN, ereal_cvg_ge0, ereal_lim_ge, ereal_lim_le
  • lemma ereal_cvg_real
  • lemmas is_cvg_ereal_nneg_series_cond, is_cvg_ereal_nneg_series, ereal_nneg_series_lim_ge0, ereal_nneg_series_pinfty
  • lemmas ereal_cvgPpinfty, ereal_cvgPninfty, lee_lim
  • lemma ereal_cvgD
    • with intermediate lemmas ereal_cvgD_pinfty_fin, ereal_cvgD_ninfty_fin, ereal_cvgD_pinfty_pinfty, ereal_cvgD_ninfty_ninfty
  • lemma ereal_limD
• in normedtype.v:
  • lemma closed_ereal_le_ereal
  • lemma closed_ereal_ge_ereal
  • lemmas natmul_continuous, cvgMn and is_cvgMn.
  • uniformType structure for ereal

Changed

• in classical_sets.v:
  • the index in bigcup_set1 generalized from nat to some Type
  • lemma bigcapCU generalized
  • lemmas preimage_setU and preimage_setI are about the setU and setI (instead of bigcup and bigcap)
  • eqEsubset changed from an implication to an equality
• lemma asboolb moved from discrete.v to boolp.v
• lemma exists2NP moved from discrete.v to boolp.v
• lemma neg_or moved from discrete.v to boolp.v and renamed to not_orP
• definitions dep_arrow_choiceClass and dep_arrow_pointedType slightly generalized and moved from topology.v to classical_sets.v
• the types of the topological notions for numFieldType have been moved from normedtype.v to topology.v
• the topology of extended real numbers has been moved from normedtype.v to ereal.v (including the notions of filters)
• numdFieldType_lalgType in normedtype.v renamed to numFieldType_lalgType in topology.v
• in ereal.v:
  • the first argument of real_of_er is now maximal implicit
  • the first argument of is_real is now maximal implicit
  • generalization of lee_sum
• in boolp.v:
  • rename exists2NP to forall2NP and make it bidirectionnal
• moved the definition of {nngnum _} and the related bigmax theory to the new nngnum.v file

Renamed

• in classical_sets.v:
  • setIDl -> setIUl
  • setUDl -> setUIl
  • setUDr -> setUIr
  • setIDr -> setIUl
  • setCE -> setTD
  • preimage_setU -> preimage_bigcup, preimage_setI -> preimage_bigcap
• in boolp.v:
  • contrap -> contra_not
  • contrapL -> contraPnot
  • contrapR -> contra_notP
  • contrapLR -> contraPP

Removed

• in boolp.v:
  • contrapNN, contrapTN, contrapNT, contrapTT
  • eqNN
• in normedtype.v:
  • forallN
  • eqNNP
  • existsN
• in discrete.v:
  • existsP
  • existsNP
• in topology.v:
  • close_to
  • close_cluster, which is subsumed by closeEnbhs

[0.3.2] - 2020-08-11

Added

• in boolp.v, new lemma andC
• in topology.v:
  • new lemma open_nbhsE
  • uniformType a structure for uniform spaces based on entourages (entourage)
  • uniformType structure on products, matrices, function spaces
  • definitions nbhs_, topologyOfEntourageMixin, split_ent, nbhsP, entourage_set, entourage_, uniformityOfBallMixin, nbhs_ball
  • lemmas nbhs_E, nbhs_entourageE, filter_from_entourageE, entourage_refl, entourage_filter, entourageT, entourage_inv, entourage_split_ex, split_entP, entourage_split_ent, subset_split_ent, entourage_split, nbhs_entourage, cvg_entourageP, cvg_entourage, cvg_app_entourageP, cvg_mx_entourageP, cvg_fct_entourageP, entourage_E, entourage_ballE, entourage_from_ballE, entourage_ball, entourage_proper_filter, open_nbhs_entourage, entourage_close
  • completePseudoMetricType structure
  • completePseudoMetricType structure on matrices and function spaces
• in classical_sets.v:
  • lemmas setICr, setUidPl, subsets_disjoint, disjoints_subset, setDidPl, setIidPl, setIS, setSI, setISS, bigcup_recl, bigcup_distrr, setMT
• in ereal.v:
  • notation \+ (ereal_scope) for function addition
  • notations > and >= for comparison of extended real numbers
  • definition is_real, lemmas is_realN, is_realD, ERFin_real_of_er, adde_undef
  • basic lemmas: addooe, adde_Neq_pinfty, adde_Neq_ninfty, addERFin, subERFin, real_of_erN, lb_ereal_inf_adherent
  • arithmetic lemmas: oppeD, subre_ge0, suber_ge0, lee_add2lE, lte_add2lE, lte_add, lte_addl, lte_le_add, lte_subl_addl, lee_subr_addr, lee_subl_addr, lte_spaddr, addeAC, addeCA
• in normedtype.v:
  • lemmas natmul_continuous, cvgMn and is_cvgMn.
  • uniformType structure for ereal
• in sequences.v:
  • definitions arithmetic, geometric
  • lemmas telescopeK, seriesK, increasing_series, cvg_shiftS, mulrn_arithmetic, exprn_geometric, cvg_arithmetic, cvg_expr, geometric_seriesE, cvg_geometric_series, is_cvg_geometric_series.

Changed

• moved from normedtype.v to boolp.v and renamed:
  • forallN -> forallNE
  • existsN -> existsNE
• topology.v:
  • unif_continuous uses entourage
  • pseudoMetricType inherits from uniformType
  • generic_source_filter and set_filter_source use entourages
  • cauchy is based on entourages and its former version is renamed cauchy_ball
  • completeType inherits from uniformType and not from pseudoMetricType
• moved from posnum.v to Rbar.v: notation posreal
• moved from normedtype.v to Rstruct.v:
  • definitions R_pointedType, R_filteredType, R_topologicalType, R_uniformType, R_pseudoMetricType
  • lemmas continuity_pt_nbhs, continuity_pt_cvg, continuity_ptE, continuity_pt_cvg', continuity_pt_nbhs', nbhs_pt_comp
  • lemmas close_trans, close_cvgxx, cvg_closeP and close_cluster are valid for a uniformType
  • moved continuous_withinNx from normedType.v to topology.v and generalised it to uniformType
• moved from measure.v to sequences.v
  • ereal_nondecreasing_series
  • ereal_nneg_series_lim_ge (renamed from series_nneg)

Renamed

• in classical_sets.v,
  • ub and lb are renamed to ubound and lbound
  • new lemmas:
    • setUCr, setCE, bigcup_set1, bigcapCU, subset_bigsetU
• in boolp.v,
  • existsPN -> not_existsP
  • forallPN -> not_forallP
  • Nimply -> not_implyP
• in classical_sets.v, ub and lb are renamed to ubound and lbound
• in ereal.v:
  • eadd -> adde, eopp -> oppe
• in topology.v:
  • locally -> nbhs
  • locally_filterE -> nbhs_filterE
  • locally_nearE -> nbhs_nearE
  • Module Export LocallyFilter -> Module Export NbhsFilter
  • locally_simpl -> nbhs_simpl
    • three occurrences
  • near_locally -> near_nbhs
  • Module Export NearLocally -> Module Export NearNbhs
  • locally_filter_onE -> nbhs_filter_onE
  • filter_locallyT -> filter_nbhsT
  • Global Instance locally_filter -> Global Instance nbhs_filter
  • Canonical locally_filter_on -> Canonical nbhs_filter_on
  • neigh -> open_nbhs
  • locallyE -> nbhsE
  • locally_singleton -> nbhs_singleton
  • locally_interior -> nbhs_interior
  • neighT -> open_nbhsT
  • neighI -> open_nbhsI
  • neigh_locally -> open_nbhs_nbhs
  • within_locallyW -> within_nbhsW
  • prod_loc_filter -> prod_nbhs_filter
  • prod_loc_singleton -> prod_nbhs_singleton
  • prod_loc_loc -> prod_nbhs_nbhs
  • mx_loc_filter -> mx_nbhs_filter
  • mx_loc_singleton -> mx_nbhs_singleton
  • mx_loc_loc -> mx_nbhs_nbhs
  • locally' -> nbhs'
  • locallyE' -> nbhsE'
  • Global Instance locally'_filter -> Global Instance nbhs'_filter
  • Canonical locally'_filter_on -> Canonical nbhs'_filter_on
  • locally_locally' -> nbhs_nbhs'
  • Global Instance within_locally_proper -> Global Instance within_nbhs_proper
  • locallyP -> nbhs_ballP
  • locally_ball -> nbhsx_ballx
  • neigh_ball -> open_nbhs_ball
  • mx_locally -> mx_nbhs
  • prod_locally -> prod_nbhs
  • Filtered.locally_op -> Filtered.nbhs_op
  • locally_of -> nbhs_of
  • open_of_locally -> open_of_nhbs
  • locally_of_open -> nbhs_of_open
  • locally_ -> nbhs_ball
  • lemma locally_ballE -> nbhs_ballE
  • locallyW -> nearW
  • nearW -> near_skip_subproof
  • locally_infty_gt -> nbhs_infty_gt
  • locally_infty_ge -> nbhs_infty_ge
  • cauchy_entouragesP -> cauchy_ballP
• in normedtype.v:
  • locallyN -> nbhsN
  • locallyC -> nbhsC
  • locallyC_ball -> nbhsC_ball
  • locally_ex -> nbhs_ex
  • Global Instance Proper_locally'_numFieldType -> Global Instance Proper_nbhs'_numFieldType
  • Global Instance Proper_locally'_realType -> Global Instance Proper_nbhs'_realType
  • ereal_locally' -> ereal_nbhs'
  • ereal_locally -> ereal_nbhs
  • Global Instance ereal_locally'_filter -> Global Instance ereal_nbhs'_filter
  • Global Instance ereal_locally_filter -> Global Instance ereal_nbhs_filter
  • ereal_loc_singleton -> ereal_nbhs_singleton
  • ereal_loc_loc -> ereal_nbhs_nbhs
  • locallyNe -> nbhsNe
  • locallyNKe -> nbhsNKe
  • locally_oo_up_e1 -> nbhs_oo_up_e1
  • locally_oo_down_e1 -> nbhs_oo_down_e1
  • locally_oo_up_1e -> nbhs_oo_up_1e
  • locally_oo_down_1e -> nbhs_oo_down_1e
  • locally_fin_out_above -> nbhs_fin_out_above
  • locally_fin_out_below -> nbhs_fin_out_below
  • locally_fin_out_above_below -> nbhs_fin_out_above_below
  • locally_fin_inbound -> nbhs_fin_inbound
  • ereal_locallyE -> ereal_nbhsE
  • locally_le_locally_norm -> nbhs_le_locally_norm
  • locally_norm_le_locally -> locally_norm_le_nbhs
  • locally_locally_norm -> nbhs_locally_norm
  • filter_from_norm_locally -> filter_from_norm_nbhs
  • locally_ball_norm -> nbhs_ball_norm
  • locally_simpl -> nbhs_simpl
  • Global Instance filter_locally -> Global Instance filter_locally
  • locally_interval -> nbhs_interval
  • ereal_locally'_le -> ereal_nbhs'_le
  • ereal_locally'_le_finite -> ereal_nbhs'_le_finite
  • locally_image_ERFin -> nbhs_image_ERFin
  • locally_open_ereal_lt -> nbhs_open_ereal_lt
  • locally_open_ereal_gt -> nbhs_open_ereal_gt
  • locally_open_ereal_pinfty -> nbhs_open_ereal_pinfty
  • locally_open_ereal_ninfty -> nbhs_open_ereal_ninfty
  • continuity_pt_locally -> continuity_pt_nbhs
  • continuity_pt_locally' -> continuity_pt_nbhs'
  • nbhs_le_locally_norm -> nbhs_le_nbhs_norm
  • locally_norm_le_nbhs -> nbhs_norm_le_nbhs
  • nbhs_locally_norm -> nbhs_nbhs_norm
  • locally_normP -> nbhs_normP
  • locally_normE -> nbhs_normE
  • near_locally_norm -> near_nbhs_norm
  • lemma locally_norm_ball_norm -> nbhs_norm_ball_norm
  • locally_norm_ball -> nbhs_norm_ball
  • pinfty_locally -> pinfty_nbhs
  • ninfty_locally -> ninfty_nbhs
  • lemma locally_pinfty_gt -> nbhs_pinfty_gt
  • lemma locally_pinfty_ge -> nbhs_pinfty_ge
  • lemma locally_pinfty_gt_real -> nbhs_pinfty_gt_real
  • lemma locally_pinfty_ge_real -> nbhs_pinfty_ge_real
  • locally_minfty_lt -> nbhs_minfty_lt
  • locally_minfty_le -> nbhs_minfty_le
  • locally_minfty_lt_real -> nbhs_minfty_lt_real
  • locally_minfty_le_real -> nbhs_minfty_le_real
  • lt_ereal_locally -> lt_ereal_nbhs
  • locally_pt_comp -> nbhs_pt_comp
• in derive.v:
  • derivable_locally -> derivable_nbhs
  • derivable_locallyP -> derivable_nbhsP
  • derivable_locallyx -> derivable_nbhsx
  • derivable_locallyxP -> derivable_nbhsxP
• in sequences.v,
  • cvg_comp_subn -> cvg_centern,
  • cvg_comp_addn -> cvg_shiftn,
  • telescoping -> telescope
  • sderiv1_series -> seriesSB
  • telescopingS0 -> eq_sum_telescope

Removed

• in topology.v:
  • definitions entourages, topologyOfBallMixin, ball_set
  • lemmas locally_E, entourages_filter, cvg_cauchy_ex

[0.3.1] - 2020-06-11

Added

• in boolp.v, lemmas for classical reasoning existsNP, existsPN, forallNP, forallPN, Nimply, orC.
• in classical_sets.v, definitions for supremums: ul, lb, supremum
• in ereal.v:
  • technical lemmas lee_ninfty_eq, lee_pinfty_eq, lte_subl_addr, eqe_oppLR
  • lemmas about supremum: ereal_supremums_neq0
  • definitions:
    • ereal_sup, ereal_inf
  • lemmas about ereal_sup:
    • ereal_sup_ub, ub_ereal_sup, ub_ereal_sup_adherent
• in normedtype.v:
  • function contract (bijection from {ereal R} to R)
  • function expand (that cancels contract)
  • ereal_pseudoMetricType R

Changed

• in reals.v, pred replaced by set from classical_sets.v
  • change propagated in many files

[0.3.0] - 2020-05-26

This release is compatible with MathComp version 1.11+beta1.

The biggest change of this release is compatibility with MathComp 1.11+beta1. The latter introduces in particular ordered types. All norms and absolute values have been unified, both in their denotation `|_| and in their theory.

Added

• sequences.v: Main theorems about sequences and series, and examples
  • Definitions:
    • [sequence E]_n is a special notation for fun n => E
    • series u_ is the sequence of partial sums
    • [normed S] is the series of absolute values, if S is a series
    • harmonic is the name of a sequence, apply series to them to get the series.
  • Theorems:
    • lots of helper lemmas to prove convergence of sequences
    • convergence of harmonic sequence
    • convergence of a series implies convergence of a sequence
    • absolute convergence implies convergence of series
• in ereal.v: lemmas about extended reals' arithmetic
• in normedtype.v: Definitions and lemmas about generic domination, boundedness, and lipschitz
  • See header for the notations and their localization
  • Added a bunch of combinators to extract existential witnesses
  • Added filter_forall (commutation between a filter and finite forall)
• about extended reals:
  • equip extended reals with a structure of topological space
  • show that extended reals are hausdorff
• in topology.v, predicate close
• lemmas about bigmaxr and argmaxr
  • \big[max/x]_P F = F [arg max_P F]
  • similar lemma for bigmin
• lemmas for within
• add setICl (intersection of set with its complement)
• prodnormedzmodule.v
  • ProdNormedZmodule transfered from MathComp
  • nonneg type for non-negative numbers
• bigmaxr/bigminr library
• Lemmas interiorI, setCU (complement of union is intersection of complements), setICl, nonsubset, setC0, setCK, setCT, preimage_setI/U, lemmas about image

Changed

• in Rstruct.v, bigmaxr is now defined using bigop
• inE now supports in_setE and in_fsetE
• fix the definition of le_ereal, lt_ereal
• various generalizations to better use the hierarchy of ssrnum (numDomainType, numFieldType, realDomainType, etc. when possible) in topology.v, normedtype.v, derive.v, etc.

Renamed

• renaming flim to cvg
  • cvg corresponds to _ --> _
  • lim corresponds to lim _
  • continuous corresponds to continuity
  • some suffixes _opp, _add ... renamed to N, D, ...
• big refactoring about naming conventions
  • complete the theory of cvg_, is_cvg_ and lim_ in normedtype.v with consistent naming schemes
  • fixed differential of inv which was defined on 1 / x instead of x^-1
  • two versions of lemmas on inverse exist
    • one in realType (Rinv_ lemmas), for which we have differential
    • a general one numFieldType (inv_ lemmas in normedtype.v, no differential so far, just continuity)
  • renamed cvg_norm to cvg_dist to reuse the name cvg_norm for convergence under the norm
• Uniform renamed to PseudoMetric
• rename is_prop to is_subset1

Removed

• sub_trans (replaced by MathComp's subrKA)
• derive.v does not require Reals anymore
• Rbar.v is almost not used anymore

Infrastructure

• NIX support
  • see config.nix, default.nix
  • for the CI also

Misc