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Changelog

Latest releases: [1.6.0] - 2024-10-25 and [1.5.0] - 2024-10-09

[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),

    • new definitions big_lexi_order, same_prefix, first_diff, big_lexi_le, and start_with.
    • new 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
    • new definitions itv_is_ray, itv_is_bd_open, and itv_open_ends
    • new 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
    • new definition order_topology
    • new 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
    • new definition completely_regular_space.
    • new 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,

    • new 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,

    • new 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,
    • new definition regular_space.
    • new 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.
    • new 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
    • new definition normal_space.
    • new lemmas filter_inv, and countable_uniform_bounded.
  • in file normedtype.v,
    • new definition edist.
    • new 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.
    • new definitions edist_inf, uniform_separator, and Urysohn.
    • new 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
    • new definitions basis, and second_countable.
    • new 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,
    • new definitions kseries, measure_fam_uub, kzero, kdirac, prob_pointed, mset, pset, pprobability, kprobability, kadd, mnormalize, knormalize, kcomp, and mkcomp.
    • new 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,
    • new definitions totally_disconnected, and zero_dimensional.
    • new lemmas component_closed, zero_dimension_prod, discrete_zero_dimension, zero_dimension_totally_disconnected, totally_disconnected_cvg, and totally_disconnected_prod.
    • new definitions split_sym, gauge, gauge_uniformType_mixin, gauge_topologicalTypeMixin, gauge_filtered, gauge_topologicalType, gauge_uniformType, gauge_pseudoMetric_mixin, and gauge_pseudoMetricType.
    • new lemmas iter_split_ent, gauge_ent, gauge_filter, gauge_refl, gauge_inv, gauge_split, gauge_countable_uniformity, and uniform_pseudometric_sup.
    • new definitions discrete_ent, discrete_uniformType, discrete_ball, discrete_pseudoMetricType, and pseudoMetric_bool.
    • new 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,
    • new definition perfect_set.
    • new lemmas perfectTP, perfect_prod, and perfect_diagonal.
    • new definitions countable_uniformity, countable_uniformityT, sup_pseudoMetric_mixin, sup_pseudoMetricType, and product_pseudoMetricType.
    • new lemmas countable_uniformityP, countable_sup_ent, and countable_uniformity_metric.
    • new definitions quotient_topology, and quotient_open.
    • new lemmas pi_continuous, quotient_continuous, and repr_comp_continuous.
    • new definitions hausdorff_accessible, separate_points_from_closed, and join_product.
    • new lemmas weak_sep_cvg, weak_sep_nbhsE, weak_sep_openE, join_product_continuous, join_product_open, join_product_inj, and join_product_weak.
    • new definition clopen.
    • new 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