{ "version": "1.0", "truncation": null, "padding": null, "added_tokens": [ { "id": 0, "content": "", "single_word": false, "lstrip": false, "rstrip": false, "normalized": false, "special": true }, { "id": 1, "content": "", "single_word": false, "lstrip": false, "rstrip": false, "normalized": false, "special": true }, { "id": 2, "content": "", "single_word": false, "lstrip": false, "rstrip": false, "normalized": false, "special": true }, { "id": 3, "content": "", "single_word": false, "lstrip": false, "rstrip": false, "normalized": false, "special": true }, { "id": 4, "content": "", "single_word": false, "lstrip": false, "rstrip": false, "normalized": false, "special": true } ], "normalizer": null, "pre_tokenizer": { "type": "WhitespaceSplit" }, "post_processor": null, "decoder": null, "model": { "type": "WordPiece", "unk_token": "", "continuing_subword_prefix": "##", "max_input_chars_per_word": 100, "vocab": { "": 0, "": 1, "": 2, "": 3, "": 4, ".": 5, "0": 6, "1": 7, "2": 8, "3": 9, "5": 10, "6": 11, "_": 12, "a": 13, "b": 14, "c": 15, "d": 16, "e": 17, "f": 18, "g": 19, "h": 20, "i": 21, "j": 22, "l": 23, "m": 24, "n": 25, "o": 26, "p": 27, "q": 28, "r": 29, "s": 30, "t": 31, "u": 32, "v": 33, "w": 34, "x": 35, "y": 36, "##u": 37, "##l": 38, "##_": 39, "##s": 40, "##i": 41, "##m": 42, "##p": 43, "##t": 44, "##a": 45, "##c": 46, "##r": 47, "##o": 48, "##b": 49, "##f": 50, "##e": 51, "##x": 52, "##h": 53, "##v": 54, "##g": 55, "##y": 56, "##.": 57, "##d": 58, "##n": 59, "##2": 60, "##j": 61, "##w": 62, "##1": 63, "##6": 64, "##q": 65, "##0": 66, "##5": 67, "##3": 68, "##_t": 69, "##ac": 70, "##_tac": 71, "##ef": 72, "##_d": 73, "##_def": 74, "##re": 75, "##in": 76, "##al": 77, "##al_": 78, "##xt": 79, "##real_": 80, "ext": 81, "extreal_": 82, "lt": 83, "##w_tac": 84, "##_in": 85, "##ft": 86, "##fty": 87, "##le": 88, "##_infty": 89, "##et": 90, "rw_tac": 91, "##is": 92, "##an": 93, "##_s": 94, "met": 95, "##is_tac": 96, "metis_tac": 97, "##ran": 98, "##_tran": 99, "##_trans": 100, "extreal_m": 101, "##lt": 102, "##ax": 103, "##en": 104, "##lt_def": 105, "##_le": 106, "##te": 107, "##le_def": 108, "##ore": 109, "d_": 110, "lt_le": 111, "lt_infty": 112, "extreal_lt_def": 113, "extreal_le_def": 114, "##on": 115, "##im": 116, "##ot": 117, "##ite": 118, "##ion": 119, "##ch": 120, "##in_def": 121, "##isch": 122, "extreal_min_def": 123, "##isch_tac": 124, "min": 125, "max": 126, "##e_trans": 127, "lte_trans": 128, "max_infty": 129, "let": 130, "##_tot": 131, "lt_tot": 132, "min_infty": 133, "let_trans": 134, "lt_total": 135, "disch_tac": 136, "##_sim": 137, "##p_tac": 138, "##rite": 139, "##write": 140, "##write_tac": 141, "sr": 142, "##bef": 143, "srw_tac": 144, "##before": 145, "gs": 146, "extreal_max": 147, "extreal_max_def": 148, "##pe": 149, "##tion": 150, "##e_": 151, "##pec": 152, "##ic": 153, "##if": 154, "##ation": 155, "gspec": 156, "##ication": 157, "##ification": 158, "gspecification": 159, "##before_def": 160, "th": 161, "then": 162, "##ul": 163, "then1": 164, "##ts": 165, "##ven": 166, "##d_s": 167, "st": 168, "##pac": 169, "##d_ss": 170, "std_ss": 171, "##or": 172, "##and": 173, "##pace": 174, "ful": 175, "##l_sim": 176, "full_sim": 177, "full_simp_tac": 178, "##_re": 179, "##ab": 180, "##_rewrite_tac": 181, "##as": 182, "##_space": 183, "##_e": 184, "##s_def": 185, "##ep": 186, "##ets_def": 187, "##orel": 188, "d_and": 189, "d_and_def": 190, "##able": 191, "##vents": 192, "##_space_def": 193, "events": 194, "d_before_def": 195, "d_or": 196, "d_or_def": 197, "re": 198, "##_n": 199, "##ar": 200, "##cl": 201, "in": 202, "##us": 203, "##ur": 204, "##eas": 205, "##clus": 206, "##urable": 207, "##easurable": 208, "##_inclus": 209, "d_sim": 210, "d_inclus": 211, "##ult_def": 212, "##_v": 213, "##iv": 214, "##e_before_def": 215, "rewrite_tac": 216, "d_simult_def": 217, "d_inclusiv": 218, "##_var": 219, "d_inclusive_before_def": 220, "##m_rewrite_tac": 221, "as": 222, "mp_tac": 223, "##sion": 224, "exten": 225, "extension": 226, "lb": 227, "measurable": 228, "##um": 229, "##of": 230, "extreal_of": 231, "##_sets_def": 232, "##_num": 233, "lborel": 234, "measurable_sets_def": 235, "extreal_of_num": 236, "extreal_of_num_def": 237, "le": 238, "le_": 239, "p_space_def": 240, "q.": 241, "##inite": 242, "le_infty": 243, "le_lt": 244, "##dep": 245, "indep": 246, "indep_var": 247, "##ex": 248, "##ists": 249, "asm_rewrite_tac": 250, "q.ex": 251, "##ists_tac": 252, "q.exists_tac": 253, "dft": 254, "dep": 255, "extreal_real_": 256, "##vent": 257, "##_event": 258, "dep_rewrite_tac": 259, "##ub": 260, "##ter": 261, "borel": 262, "sub": 263, "##sets_def": 264, "##ma": 265, "##_inter": 266, "dft_event": 267, "extreal_real_le": 268, "subsets_def": 269, "finite": 270, "m_space_def": 271, "nor": 272, "##mal_": 273, "##ing": 274, "events_def": 275, "normal_": 276, "##ct": 277, "##om": 278, "##real": 279, "##_sing": 280, "gen": 281, "pr": 282, "##lim": 283, "##hm": 284, "##_thm": 285, "##_elim": 286, "normal_real": 287, "gen_tac": 288, "pro": 289, "##ig": 290, "events_inter": 291, "indep_vars": 292, "et": 293, "se": 294, "sig": 295, "##_c": 296, "##ag": 297, "##a_thm": 298, "##nd": 299, "##lect": 300, "##et_tac": 301, "##imag": 302, "##ot_infty": 303, "##ma_def": 304, "dft_event_def": 305, "finite_sing": 306, "##_elim_tac": 307, "eta_thm": 308, "select": 309, "sigma_def": 310, "select_elim_tac": 311, "eq": 312, "##un": 313, "##_m": 314, "##ve": 315, "prob": 316, "eq_tac": 317, "on": 318, "rand": 319, "space": 320, "und": 321, "##_before": 322, "##iab": 323, "##table": 324, "##ce_": 325, "##oun": 326, "##finite": 327, "##gt": 328, "##reimag": 329, "##ist": 330, "##asm_rewrite_tac": 331, "events_space": 332, "in_m": 333, "##_variab": 334, "lborel_le": 335, "##om_variab": 336, "prob_": 337, "once_": 338, "random_variab": 339, "space_def": 340, "undisch_tac": 341, "##ountable": 342, "in_measurable": 343, "once_asm_rewrite_tac": 344, "random_variable_def": 345, "##_p": 346, "##_as": 347, "##so": 348, "##m_s": 349, "##dd": 350, "extreal_le": 351, "##_eq": 352, "asm_s": 353, "##gt0": 354, "##_asso": 355, "extreal_le_eq": 356, "asm_set_tac": 357, "##_assoc": 358, "cd": 359, "mul": 360, "ne": 361, "pi": 362, "preimag": 363, "##_gt0": 364, "##r_def": 365, "##f_def": 366, "##ext": 367, "##e_le": 368, "##ym": 369, "##not_infty": 370, "extreal_mul": 371, "gsym": 372, "##_not_infty": 373, "##omm": 374, "##_countable": 375, "##_comm": 376, "##ver_def": 377, "prob_finite": 378, "cdf_def": 379, "never_def": 380, "pie_le": 381, "extreal_mul_def": 382, "pie_lem": 383, "al": 384, "add": 385, "con": 386, "car": 387, "ps": 388, "##l_d": 389, "##_and": 390, "##se": 391, "##inct": 392, "extreal_not_infty": 393, "##e_ext": 394, "dft_event_and": 395, "prove": 396, "##istinct": 397, "preimage_ext": 398, "pie_lemma": 399, "all_d": 400, "conj": 401, "pset_tac": 402, "dft_event_and_before": 403, "preimage_extreal_": 404, "all_distinct": 405, "and": 406, "countable": 407, "dist": 408, "ima": 409, "me": 410, "not": 411, "po": 412, "rv": 413, "##ution": 414, "##_l": 415, "##_imag": 416, "##ss": 417, "##ir": 418, "##ib": 419, "##mp": 420, "##mul": 421, "##ty": 422, "##add": 423, "##air": 424, "##rv": 425, "##rib": 426, "##ose": 427, "##ge_": 428, "##2rv": 429, "##infty": 430, "##al_ss": 431, "##real_mul": 432, "##real_2rv": 433, "##ispec": 434, "min_comm": 435, "##_emp": 436, "events_countable": 437, "real": 438, "real_ss": 439, "##_ninfty": 440, "in_elim": 441, "q.ispec": 442, "dft_before": 443, "extreal_real_lt": 444, "##_event_gt0": 445, "finite_def": 446, "finite_countable": 447, "normal_real_mul": 448, "##_sing_emp": 449, "##_preimag": 450, "##_pair": 451, "mul_not_infty": 452, "##_gt0_ninfty": 453, "add_assoc": 454, "card": 455, "conj_assoc": 456, "dft_event_and_before_preimag": 457, "preimage_extreal_real_2rv": 458, "and_inter": 459, "countable_imag": 460, "distrib": 461, "image_": 462, "mem": 463, "not_sing_emp": 464, "rv_gt0_ninfty": 465, "##ution_def": 466, "##osed": 467, "events_countable_inter": 468, "in_elim_pair": 469, "q.ispecl": 470, "dft_before_event_gt0": 471, "countable_image": 472, "distribution_def": 473, "image_finite": 474, "not_sing_empty": 475, "rv_gt0_ninfty_def": 476, "in_elim_pair_thm": 477 } } }