| { |
| "created": "2026-10-17", |
| "split": "dev", |
| "n": 20, |
| "sample_seed": 2026, |
| "depth": 16, |
| "tool": "lean-lsp-mcp 0.31.0 lean_leansearch (leansearch.net), query = signature text", |
| "note": "LeanSearch indexes all of Mathlib (incl. the query theorem, defs, instances) and may lag our pinned commit; the query itself is removed before scoring", |
| "items": [ |
| { |
| "name": "LinearMap.BilinForm.sum_left", |
| "gold": [ |
| "LinearMap.map_sum₂" |
| ], |
| "leansearch": [ |
| "LinearMap.BilinForm.sum_left", |
| "LinearMap.BilinForm.sum_right", |
| "LinearMap.BilinForm.add_left", |
| "LinearMap.BilinForm.sum_apply", |
| "LinearMap.map_sum₂", |
| "LinearMap.BilinForm.add_right", |
| "LinearMap.BilinForm.add_apply", |
| "LinearMap.BilinForm.comp_apply", |
| "LinearMap.BilinForm", |
| "LinearMap.BilinForm.comp", |
| "QuadraticMap.add_toBilin", |
| "LinearMap.BilinForm.sum_repr_mul_repr_mul", |
| "LinearMap.BilinForm.comp_id_id", |
| "LinearMap.BilinForm.linMulLin_apply", |
| "LinearMap.BilinForm.coeFnAddMonoidHom_apply", |
| "Finsupp.bilinearCombination" |
| ], |
| "bm25": [ |
| "LinearMap.BilinForm.sum_right", |
| "LinearMap.BilinForm.sum_apply", |
| "LinearMap.BilinMap.toQuadraticMap_sum", |
| "LinearMap.BilinForm.congr_congr", |
| "LinearMap.BilinForm.comp_apply", |
| "LinearMap.BilinForm.compRight_apply", |
| "LinearMap.BilinForm.compLeft_apply", |
| "LinearMap.BilinForm.iIsOrtho_def", |
| "LinearMap.BilinForm.congr_apply", |
| "LinearMap.BilinForm.linMulLin_comp", |
| "LinearMap.BilinForm.congr_symm", |
| "Derivation.coe_sum_linearMap", |
| "LinearMap.BilinForm.isSymm_iff_flip", |
| "LinearMap.BilinForm.inf_orthogonal_self_le_ker_restrict", |
| "LinearMap.BilinForm.orthogonal_bot", |
| "LinearMap.BilinForm.compLeft_id" |
| ], |
| "rrf_bm25_e5_instr": [ |
| "LinearMap.BilinForm.sum_right", |
| "LinearMap.BilinForm.sum_apply", |
| "LinearMap.BilinForm.compRight_apply", |
| "LinearMap.BilinForm.congr_congr", |
| "LinearMap.BilinForm.congr_symm", |
| "LinearMap.BilinForm.congr_apply", |
| "LinearMap.BilinForm.compLeft_apply", |
| "LinearMap.BilinForm.comp_apply", |
| "LinearMap.BilinForm.congr_comp", |
| "LinearMap.BilinForm.comp_comp", |
| "LinearMap.BilinForm.linMulLin_comp", |
| "LinearMap.BilinForm.comp_congr", |
| "Derivation.coe_sum_linearMap", |
| "LinearMap.BilinForm.compLeft_id", |
| "LinearMap.sum_apply", |
| "LinearMap.BilinForm.orthogonal_bot" |
| ] |
| }, |
| { |
| "name": "DirichletCharacter.delta_mul", |
| "gold": [ |
| "DirichletCharacter.mul_delta" |
| ], |
| "leansearch": [ |
| "DirichletCharacter.delta_mul", |
| "DirichletCharacter.mul_delta", |
| "LSeries.delta_mul", |
| "LSeries.mul_delta_eq_smul_delta", |
| "DirichletCharacter.modZero_eq_delta", |
| "LSeries_delta", |
| "DirichletCharacter.LFunction_modOne_eq", |
| "DirichletCharacter.convolution_mul_moebius", |
| "ArithmeticFunction.one_eq_delta", |
| "DirichletCharacter.LSeries_modOne_eq", |
| "LSeries.term_delta", |
| "DirichletCharacter.deriv_LFunction_eq_deriv_LSeries", |
| "DirichletCharacter.LFunction_eq_LSeries", |
| "DirichletCharacter.zetaMul", |
| "DirichletCharacter.LSeriesSummable_mul", |
| "DirichletCharacter.completedLFunction.congr_simp" |
| ], |
| "bm25": [ |
| "DirichletCharacter.mul_delta", |
| "DirichletCharacter.modZero_eq_delta", |
| "DirichletCharacter.convolution_mul_moebius", |
| "DirichletCharacter.LSeries.mul_mu_eq_one", |
| "DirichletCharacter.deriv_LFunction_eq_deriv_LSeries", |
| "DirichletCharacter.LSeriesSummable_mul", |
| "DirichletCharacter.LFunction_eq_LSeries", |
| "DirichletCharacter.LSeries_twist_vonMangoldt_eq", |
| "DirichletCharacter.LSeriesSummable_twist_vonMangoldt", |
| "DirichletCharacter.LSeriesSummable_of_one_lt_re", |
| "tsum_dirichletSummand", |
| "DirichletCharacter.LSeries_changeLevel", |
| "DirichletCharacter.LSeries_eulerProduct_exp_log", |
| "DirichletCharacter.LSeries_eq_exp_LSeries", |
| "DirichletCharacter.LSeries_ne_zero_of_one_lt_re", |
| "DirichletCharacter.not_LSeriesSummable_at_one" |
| ], |
| "rrf_bm25_e5_instr": [ |
| "DirichletCharacter.mul_delta", |
| "DirichletCharacter.modZero_eq_delta", |
| "DirichletCharacter.deriv_LFunction_eq_deriv_LSeries", |
| "DirichletCharacter.convolution_mul_moebius", |
| "DirichletCharacter.LSeries.mul_mu_eq_one", |
| "tsum_dirichletSummand", |
| "DirichletCharacter.LFunction_eq_LSeries", |
| "DirichletCharacter.LSeries_eq_exp_LSeries", |
| "DirichletCharacter.LSeriesSummable_zetaMul", |
| "DirichletCharacter.LSeries_modOne_eq", |
| "DirichletCharacter.mul_convolution_distrib", |
| "DirichletCharacter.LSeries_changeLevel", |
| "DirichletCharacter.convolution_twist_vonMangoldt", |
| "DirichletCharacter.LSeriesSummable_mul", |
| "DirichletCharacter.LSeries_twist_vonMangoldt_eq", |
| "LSeries.mul_delta" |
| ] |
| }, |
| { |
| "name": "Finset.truncatedSup_union_of_notMem", |
| "gold": [ |
| "Finset.truncatedSup_of_notMem" |
| ], |
| "leansearch": [ |
| "Finset.truncatedSup_of_notMem", |
| "Finset.truncatedSup_union_of_notMem", |
| "Finset.truncatedSup_union_right", |
| "Finset.truncatedSup", |
| "Finset.truncatedSup_union", |
| "Finset.truncatedSup_infs_of_notMem", |
| "Finset.truncatedSup_union_left", |
| "Finset.truncatedInf_union_of_notMem", |
| "Finset.truncatedSup_of_mem", |
| "Finset.truncatedInf_union_left", |
| "Finset.truncatedInf_of_notMem", |
| "Finset.filter_sups_le", |
| "Finset.truncatedSup_singleton", |
| "Finset.truncatedSup_of_isAntichain", |
| "Finset.truncatedSup_empty", |
| "Finset.truncatedInf_union_right" |
| ], |
| "bm25": [ |
| "Finset.truncatedSup_union_right", |
| "Finset.truncatedSup_union_left", |
| "Finset.truncatedSup_union", |
| "Finset.truncatedInf_union_of_notMem", |
| "Finset.truncatedSup_of_notMem", |
| "Finset.truncatedInf_union_right", |
| "Finset.truncatedInf_union_left", |
| "Finset.truncatedSup_infs", |
| "Finset.truncatedSup_infs_of_notMem", |
| "Finset.truncatedInf_union", |
| "Finset.truncatedSup_of_mem", |
| "Finset.truncatedInf_sups", |
| "Finset.truncatedSup_empty", |
| "Finset.truncatedInf_sups_of_notMem", |
| "Finset.le_truncatedSup", |
| "Finset.truncatedInf_of_notMem" |
| ], |
| "rrf_bm25_e5_instr": [ |
| "Finset.truncatedSup_union_right", |
| "Finset.truncatedSup_union_left", |
| "Finset.truncatedSup_of_notMem", |
| "Finset.truncatedSup_union", |
| "Finset.truncatedInf_union_right", |
| "Finset.truncatedInf_union_left", |
| "Finset.truncatedInf_union_of_notMem", |
| "Finset.truncatedSup_of_mem", |
| "Finset.truncatedSup_empty", |
| "Finset.le_truncatedSup", |
| "Finset.truncatedInf_union", |
| "Finset.truncatedSup_infs", |
| "Finset.truncatedSup_infs_of_notMem", |
| "Finset.truncatedSup_singleton", |
| "Finset.truncatedInf_of_notMem", |
| "Finset.truncatedInf_sups" |
| ] |
| }, |
| { |
| "name": "Fin.card_filter_univ_succ", |
| "gold": [ |
| "Fin.univ_succ", |
| "Finset.card_cons", |
| "Finset.card_map", |
| "Finset.filter_cons", |
| "Finset.filter_map" |
| ], |
| "leansearch": [ |
| "Fin.card_filter_univ_succ", |
| "Fin.card_filter_univ_succ'", |
| "Nat.count_succ", |
| "Nat.count_succ'", |
| "Nat.count_succ_eq_succ_count", |
| "Nat.count_succ_eq_succ_count_iff", |
| "Fintype.card_subtype", |
| "Nat.count_eq_card_filter_range", |
| "Nat.count_eq_card_fintype", |
| "Nat.count_lt_card", |
| "Finset.sum_boole", |
| "Finset.card_filter", |
| "Nat.count_succ_eq_count_iff", |
| "Finite.card_subtype_le", |
| "Nat.count", |
| "Nat.count_le_cardinal" |
| ], |
| "bm25": [ |
| "Fin.card_filter_univ_succ'", |
| "Fin.find_eq_dite", |
| "Nat.count_succ", |
| "Nat.count_succ'", |
| "Nat.findGreatest_succ", |
| "Finset.card_consEquiv_filter_piFinset", |
| "Finset.card_filter", |
| "Finset.card_snocEquiv_filter_piFinset", |
| "Fin.find?_decide_eq_dite", |
| "Finset.card_insertNthEquiv_filter_piFinset", |
| "Finset.natCast_card_filter", |
| "Finset.sum_boole", |
| "Nat.count_one", |
| "Fin.predAbove_zero", |
| "Fin.find_of_not_zero", |
| "coe_finRotate" |
| ], |
| "rrf_bm25_e5_instr": [ |
| "Fin.card_filter_univ_succ'", |
| "Fin.find_eq_dite", |
| "Finset.card_filter", |
| "Fin.find_of_not_zero", |
| "Finset.card_consEquiv_filter_piFinset", |
| "Finset.card_insertNthEquiv_filter_piFinset", |
| "Nat.count_nth_succ", |
| "Finset.sum_boole", |
| "Fin.find_eq_zero", |
| "Fin.find_pos", |
| "Nat.findGreatest_succ", |
| "Finset.natCast_card_filter", |
| "Finset.card_snocEquiv_filter_piFinset", |
| "Nat.count_succ", |
| "Nat.count_eq_card_filter_range", |
| "Fin.find?_decide_eq_dite" |
| ] |
| }, |
| { |
| "name": "Int.natCast_mul_floor_div_cancel", |
| "gold": [ |
| "Int.mul_natCast_floor_div_cancel", |
| "Nat.cast_comm" |
| ], |
| "leansearch": [ |
| "Int.natCast_mul_floor_div_cancel", |
| "Int.mul_natCast_floor_div_cancel", |
| "Int.mul_cast_floor_div_cancel_of_pos", |
| "Nat.cast_mul_floor_div_cancel", |
| "Nat.mul_cast_floor_div_cancel", |
| "Int.cast_mul_floor_div_cancel_of_pos", |
| "Int.floor_div_natCast", |
| "Int.floorRing_floor_eq", |
| "FloorRing.floor", |
| "Int.floor", |
| "Int.floor_ofNat_add", |
| "Int.floor_div_cast_of_nonneg", |
| "Nat.floor_div_natCast", |
| "Int.floor_natCast_add", |
| "Int.floor_sub_natCast", |
| "Int.floor_add_ofNat" |
| ], |
| "bm25": [ |
| "Int.mul_natCast_floor_div_cancel", |
| "Int.cast_mul_floor_div_cancel_of_pos", |
| "Int.mul_cast_floor_div_cancel_of_pos", |
| "Nat.mul_cast_floor_div_cancel", |
| "Nat.cast_mul_floor_div_cancel", |
| "Int.floor_div_cast_of_nonneg", |
| "Int.floor_div_natCast", |
| "Int.floor_add_natCast", |
| "Int.floor_natCast_add", |
| "Int.floor_sub_natCast", |
| "Int.sum_floor_add_div", |
| "Nat.floor_div_natCast", |
| "Nat.floor_add_natCast", |
| "Int.floor_add_intCast", |
| "Int.floor_intCast_add", |
| "Int.le_floor_add_floor" |
| ], |
| "rrf_bm25_e5_instr": [ |
| "Int.mul_natCast_floor_div_cancel", |
| "Int.floor_sub_natCast", |
| "Int.floor_natCast_add", |
| "Int.cast_mul_floor_div_cancel_of_pos", |
| "Int.mul_cast_floor_div_cancel_of_pos", |
| "Int.floor_add_natCast", |
| "Nat.abs_floor_sub_le", |
| "Int.floor_sub_one", |
| "Int.floor_sub_ofNat", |
| "Int.sub_one_lt_floor", |
| "Int.ceil_neg", |
| "Int.floor_neg", |
| "Nat.abs_sub_floor_le", |
| "Int.le_floor_add", |
| "Int.floor_sub_intCast", |
| "Nat.zero_le_self_sub_floor" |
| ] |
| }, |
| { |
| "name": "Nat.dvd_of_primeFactorsList_subperm", |
| "gold": [ |
| "LT.lt.ne'", |
| "List.Perm.prod_eq", |
| "Nat.prod_primeFactorsList", |
| "dvd_zero", |
| "one_dvd" |
| ], |
| "leansearch": [ |
| "Nat.dvd_of_primeFactorsList_subperm", |
| "Nat.factorization_le_iff_dvd", |
| "Nat.dvd_of_mem_primeFactorsList", |
| "Nat.dvd_of_mem_primeFactors", |
| "Nat.factorization_prime_le_iff_dvd", |
| "Nat.mem_primeFactorsList_iff_dvd", |
| "PNat.factorMultiset_le_iff'", |
| "Nat.primeFactorsList_sublist_of_dvd", |
| "PNat.factorMultiset_le_iff", |
| "UniqueFactorizationMonoid.dvd_of_mem_normalizedFactors", |
| "UniqueFactorizationMonoid.dvd_of_mem_factors", |
| "Nat.dvd_iff_div_factorization_eq_tsub", |
| "Nat.replicate_subperm_primeFactorsList_iff", |
| "Nat.primeFactors_filter_dvd_of_dvd", |
| "Nat.prod_primeFactors_dvd", |
| "Nat.primeFactorsList_subset_of_dvd" |
| ], |
| "bm25": [ |
| "Nat.replicate_subperm_primeFactorsList_iff", |
| "le_emultiplicity_iff_replicate_subperm_primeFactorsList", |
| "le_padicValNat_iff_replicate_subperm_primeFactorsList", |
| "Nat.eq_of_perm_primeFactorsList", |
| "Nat.mem_primeFactorsList_mul", |
| "Nat.perm_primeFactorsList_mul", |
| "Nat.primeFactorsList_subset_of_dvd", |
| "Nat.primeFactorsList_sublist_of_dvd", |
| "Nat.primeFactors_mul", |
| "Nat.mem_primeFactorsList_mul_right", |
| "Nat.primeFactors_gcd", |
| "Nat.disjoint_primeFactors", |
| "Nat.mem_primeFactorsList", |
| "Nat.mem_primeFactorsList'", |
| "Nat.mem_primeFactorsList_iff_dvd", |
| "Nat.primeFactorsList_subset_right" |
| ], |
| "rrf_bm25_e5_instr": [ |
| "Nat.replicate_subperm_primeFactorsList_iff", |
| "Nat.eq_of_perm_primeFactorsList", |
| "le_emultiplicity_iff_replicate_subperm_primeFactorsList", |
| "le_padicValNat_iff_replicate_subperm_primeFactorsList", |
| "Nat.mem_primeFactorsList_mul", |
| "Nat.primeFactors_mul", |
| "Nat.perm_primeFactorsList_mul", |
| "Nat.mem_primeFactorsList_mul_right", |
| "Nat.primeFactorsList_sublist_of_dvd", |
| "Nat.primeFactorsList_sublist_right", |
| "Nat.disjoint_primeFactors", |
| "Nat.primeFactors_gcd", |
| "Nat.mem_primeFactorsList_mul_left", |
| "Nat.primeFactorsList_subset_right", |
| "Nat.primeFactorsList_subset_of_dvd", |
| "Nat.mem_primeFactorsList" |
| ] |
| }, |
| { |
| "name": "Nat.sum_range_choose", |
| "gold": [ |
| "add_pow", |
| "one_add_one_eq_two" |
| ], |
| "leansearch": [ |
| "Nat.sum_range_choose", |
| "Nat.sum_range_add_choose", |
| "Finset.sum_powerset_apply_card", |
| "Finset.sum_choose_succ_nsmul", |
| "Nat.choose_le_two_pow", |
| "Fintype.sum_pow_mul_eq_add_pow", |
| "add_pow", |
| "Finset.sum_pow_mul_eq_add_pow", |
| "Finset.sum_choose_succ_mul", |
| "Fin.sum_pow_mul_eq_add_pow", |
| "Nat.sum_range_choose_halfway", |
| "Int.alternating_sum_range_choose", |
| "Nat.sum_Icc_choose", |
| "Int.alternating_sum_range_choose_of_ne", |
| "Commute.add_pow'", |
| "Int.alternating_sum_range_choose_eq_choose" |
| ], |
| "bm25": [ |
| "Int.alternating_sum_range_choose_eq_choose", |
| "Finset.sum_choose_succ_nsmul", |
| "Nat.sum_range_choose_halfway", |
| "Int.alternating_sum_range_choose", |
| "Int.alternating_sum_range_choose_of_ne", |
| "Finset.prod_pow_choose_succ", |
| "Nat.sum_range_choose_sq", |
| "Nat.sum_range_mul_choose", |
| "add_pow", |
| "Polynomial.geom_sum_X_comp_X_add_one_eq_sum", |
| "Finset.sum_choose_succ_mul", |
| "sum_range_shift_eq_sum_fwdDiff_iter", |
| "Finset.sum_antidiagonal_choose_succ_nsmul", |
| "sub_pow", |
| "Nat.sum_range_multichoose", |
| "Finset.prod_antidiagonal_pow_choose_succ" |
| ], |
| "rrf_bm25_e5_instr": [ |
| "Nat.sum_range_choose_halfway", |
| "Int.alternating_sum_range_choose", |
| "Int.alternating_sum_range_choose_eq_choose", |
| "Nat.sum_range_mul_choose", |
| "Finset.prod_pow_choose_succ", |
| "Int.alternating_sum_range_choose_of_ne", |
| "Finset.sum_choose_succ_nsmul", |
| "Nat.sum_range_multichoose", |
| "Nat.sum_range_choose_sq", |
| "add_pow", |
| "bernoulli'_def", |
| "sub_pow", |
| "Nat.uniformBell_eq", |
| "bernoulli'_spec", |
| "Finset.sum_range_succ", |
| "sum_bernoulli'" |
| ] |
| }, |
| { |
| "name": "Finset.three_lt_card_iff", |
| "gold": [ |
| "Finset.card_eq_four", |
| "Finset.insert_subset_iff", |
| "Finset.le_card_iff_exists_subset_card" |
| ], |
| "leansearch": [ |
| "Finset.three_lt_card_iff", |
| "Finset.three_lt_card", |
| "Set.three_lt_ncard_iff", |
| "Set.three_lt_ncard", |
| "Finset.two_lt_card_iff", |
| "Set.two_lt_ncard", |
| "Finset.two_lt_card", |
| "Finset.card_eq_three", |
| "Set.two_lt_ncard_iff", |
| "Finset.card_eq_four", |
| "Finset.le_card_iff_exists_subset_card", |
| "Set.ncard_eq_four", |
| "Fintype.two_lt_card_iff", |
| "Set.ncard_eq_three", |
| "Finset.one_lt_card_iff", |
| "Finset.card_le_four" |
| ], |
| "bm25": [ |
| "Finset.three_lt_card", |
| "Finset.two_lt_card", |
| "Finset.two_lt_card_iff", |
| "Set.three_lt_ncard", |
| "Finset.one_lt_card_iff", |
| "Set.three_lt_ncard_iff", |
| "Finset.one_lt_card", |
| "Fintype.two_lt_card_iff", |
| "Set.two_lt_ncard", |
| "Set.two_lt_ncard_iff", |
| "Finset.exists_mem_ne", |
| "Finset.card_triple_eq_three_iff", |
| "Finset.card_eq_three", |
| "Finset.Colex.toColex_lt_toColex", |
| "Finset.card_le_card_of_forall_subsingleton", |
| "Finset.card_le_card_of_forall_subsingleton'" |
| ], |
| "rrf_bm25_e5_instr": [ |
| "Finset.three_lt_card", |
| "Finset.two_lt_card", |
| "Finset.two_lt_card_iff", |
| "Finset.one_lt_card", |
| "Finset.one_lt_card_iff", |
| "Finset.card_eq_three", |
| "Finset.card_le_card_of_forall_subsingleton", |
| "Finset.card_le_card_of_forall_subsingleton'", |
| "Finset.exists_mem_ne", |
| "Finset.card_le_one", |
| "Finset.card_eq_succ", |
| "Finset.card_eq_one_iff_existsUnique", |
| "Finset.card_le_one_iff", |
| "Finset.card_triple_eq_three_iff", |
| "Finset.card_eq_four", |
| "Finset.card_eq_two" |
| ] |
| }, |
| { |
| "name": "Finset.sup_product_right", |
| "gold": [ |
| "Finset.sup_comm", |
| "Finset.sup_product_left" |
| ], |
| "leansearch": [ |
| "Finset.sup_product_right", |
| "Finset.sup_product_left", |
| "Finset.sup'_product_right", |
| "biSup_prod'", |
| "Finset.sup'_product_left", |
| "Finset.sup_image₂_right", |
| "biSup_prod", |
| "Finset.sup_mul_right", |
| "Finset.sup_mul_left", |
| "iSup_prod", |
| "Finset.sup_prodMap", |
| "Finset.sup_sigma", |
| "Finset.sup_add_right", |
| "sSup_image2", |
| "Finset.image_sup_product", |
| "Finset.sup'_prodMap" |
| ], |
| "bm25": [ |
| "Finset.sup_product_left", |
| "Finset.sup'_product_right", |
| "Finset.sup'_product_left", |
| "Finset.inf_product_left", |
| "Finset.inf_product_right", |
| "Finset.inf'_product_right", |
| "Finset.inf'_product_left", |
| "Finset.sup_comm", |
| "Finset.sup_sigma", |
| "Finset.sup_biUnion", |
| "Finset.SupIndep.product", |
| "Finset.sup_disjSum", |
| "Finset.sup_image₂_right", |
| "Finset.sup_image₂_left", |
| "Finset.sup_prodMap", |
| "Finset.sup'_comm" |
| ], |
| "rrf_bm25_e5_instr": [ |
| "Finset.sup_comm", |
| "Finset.sup_sigma", |
| "Finset.sup_product_left", |
| "Finset.sup'_product_right", |
| "Finset.sup_attach", |
| "Finset.sup_sub_left", |
| "Finset.sup_sub_right", |
| "Finset.sup_disjSum", |
| "Finset.sup_inv", |
| "Finset.sup'_product_left", |
| "Finset.sup_const_le", |
| "Finset.sup_image₂_right", |
| "Finset.sup_div_right", |
| "Finset.sup_div_left", |
| "Finset.sup_image₂_left", |
| "Finset.sup_mono_fun" |
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| "Nat.prod_primeFactors_prod_factorization", |
| "ArithmeticFunction.IsMultiplicative.prodPrimeFactors", |
| "Multipliable.tendsto_prod_tprod_nat", |
| "EulerProduct.eulerProduct_tprod", |
| "Multipliable.tprod_eq_mul_tprod_ite", |
| "ArithmeticFunction.IsMultiplicative.eulerProduct_tprod", |
| "tprod_eq_tprod_primes_of_mulSupport_subset_prime_powers", |
| "tprod_eq_tprod_primes_mul_tprod_primes_of_mulSupport_subset_prime_powers", |
| "tprod_eq_prod", |
| "prod_eq_tprod_mulIndicator", |
| "ArithmeticFunction.IsMultiplicative.eulerProduct_hasProd", |
| "EulerProduct.prod_filter_prime_geometric_eq_tsum_factoredNumbers" |
| ], |
| "bm25": [ |
| "Nat.Primes.tsum_eq_tsum_ite", |
| "Nat.Primes.multipliable_iff_multipliable_ite", |
| "Nat.Primes.summable_iff_summable_ite", |
| "Nat.Primes.hasProd_iff_hasProd_ite", |
| "Nat.Primes.hasSum_iff_hasSum_ite", |
| "tprod_eq_tprod_primes_mul_tprod_primes_of_mulSupport_subset_prime_powers", |
| "tprod_primes_pow_eq", |
| "Nat.primesBelow_succ", |
| "tprod_eq_tprod_primes_of_mulSupport_subset_prime_powers", |
| "Nat.primesLE_succ", |
| "Nat.cast_ite", |
| "tsum_eq_tsum_primes_add_tsum_primes_of_support_subset_prime_powers", |
| "EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_tsum", |
| "Nat.Partition.powerSeriesMk_card_restricted_eq_tprod", |
| "EulerProduct.eulerProduct_completely_multiplicative_tprod", |
| "tprod_dite_left" |
| ], |
| "rrf_bm25_e5_instr": [ |
| "Nat.Primes.multipliable_iff_multipliable_ite", |
| "Nat.Primes.tsum_eq_tsum_ite", |
| "Nat.Primes.hasProd_iff_hasProd_ite", |
| "Nat.Primes.summable_iff_summable_ite", |
| "Nat.Primes.hasSum_iff_hasSum_ite", |
| "Nat.cast_ite", |
| "tprod_nat_mul_neg_add_one", |
| "tprod_pnat_eq_tprod_succ", |
| "tprod_pnat_eq_tprod_of_eq_one", |
| "tprod_nat_mul_neg", |
| "tprod_dite_right", |
| "tprod_of_nat_of_neg_add_one", |
| "tprod_dite_left", |
| "finprod_eq_dif", |
| "Finset.ite_prod_one", |
| "finprod_eq_if" |
| ] |
| }, |
| { |
| "name": "Nat.Prime.sub_one_mul_multiplicity_factorial", |
| "gold": [ |
| "Finset.sum_Ico_add'", |
| "Nat.Ico_zero_eq_range", |
| "Nat.Prime.emultiplicity_factorial", |
| "Nat.sub_one_mul_sum_log_div_pow_eq_sub_sum_digits", |
| "multiplicity_eq_of_emultiplicity_eq_some" |
| ], |
| "leansearch": [ |
| "Nat.Prime.sub_one_mul_multiplicity_factorial", |
| "sub_one_mul_padicValNat_factorial", |
| "Nat.sub_one_mul_factorization_factorial", |
| "padicValNat_factorial", |
| "padicValNat_factorial_le", |
| "sub_one_mul_padicValNat_factorial_lt_of_ne_zero", |
| "padicValNat_factorial_lt_of_ne_zero", |
| "Nat.sub_one_mul_sum_log_div_pow_eq_sub_sum_digits", |
| "Nat.Prime.multiplicity_factorial_pow", |
| "padicValNat_def", |
| "Nat.multiplicity_eq_factorization", |
| "Nat.factorization_factorial", |
| "Nat.Prime.emultiplicity_factorial_mul", |
| "Nat.factorization_def", |
| "padicValNat_factorial_mul", |
| "padicValNat_mul_div_factorial" |
| ], |
| "bm25": [ |
| "sub_one_mul_padicValNat_factorial", |
| "Nat.sub_one_mul_factorization_factorial", |
| "Nat.Prime.multiplicity_factorial_pow", |
| "Nat.Prime.emultiplicity_factorial_mul_succ", |
| "Nat.Prime.emultiplicity_factorial_mul", |
| "sub_one_mul_padicValNat_choose_eq_sub_sum_digits'", |
| "Nat.Prime.emultiplicity_factorial", |
| "Nat.factorization_factorial", |
| "Nat.Prime.emultiplicity_factorial_le_div_pred", |
| "sub_one_mul_padicValNat_factorial_lt_of_ne_zero", |
| "Nat.factorization_factorial_le_div_pred", |
| "padicValNat_factorial_mul_add", |
| "padicValNat_factorial_mul", |
| "Nat.sub_one_mul_sum_log_div_pow_eq_sub_sum_digits", |
| "padicValNat_mul_div_factorial", |
| "padicValNat_factorial_le" |
| ], |
| "rrf_bm25_e5_instr": [ |
| "Nat.Prime.multiplicity_factorial_pow", |
| "Nat.sub_one_mul_factorization_factorial", |
| "Nat.Prime.emultiplicity_factorial_mul_succ", |
| "sub_one_mul_padicValNat_factorial", |
| "Nat.Prime.emultiplicity_factorial_mul", |
| "Nat.Prime.emultiplicity_factorial", |
| "Nat.factorization_factorial", |
| "Nat.Prime.emultiplicity_factorial_le_div_pred", |
| "Nat.factorization_factorial_le_div_pred", |
| "Nat.Prime.coprime_factorial_of_lt", |
| "Nat.multiplicity_eq_factorization", |
| "Nat.Prime.factorization_self", |
| "Nat.factorization_factorial_mul_succ", |
| "padicValNat_factorial_le", |
| "Nat.digit_sum_le", |
| "padicValNat_factorial_mul_add" |
| ] |
| }, |
| { |
| "name": "SimpleGraph.zarankiewicz_le_iff_of_nonneg", |
| "gold": [ |
| "Nat.le_floor_iff", |
| "SimpleGraph.zarankiewicz_le_iff" |
| ], |
| "leansearch": [ |
| "SimpleGraph.extremalNumber_le_iff_of_nonneg", |
| "SimpleGraph.extremalNumber_le_iff", |
| "SimpleGraph.card_edgeFinset_le_extremalNumber", |
| "SimpleGraph.extremalNumber_of_fintypeCard_eq", |
| "SimpleGraph.extremalNumber", |
| "SimpleGraph.completeBipartiteGraph_isContained_iff", |
| "SimpleGraph.lt_extremalNumber_iff", |
| "SimpleGraph.card_edgeFinset_eq_extremalNumber_top_iff_nonempty_iso_turanGraph", |
| "SimpleGraph.lt_extremalNumber_iff_of_nonneg", |
| "SimpleGraph.extremalNumber_top", |
| "SimpleGraph.isExtremal_top_free_iff_isTuranMaximal", |
| "SimpleGraph.edgeDensity_le_one", |
| "SimpleGraph.Copy.completeBipartiteGraph", |
| "SimpleGraph.card_edgeFinset_le_card_choose_two", |
| "SimpleGraph.isBipartiteWith_degree_le", |
| "SimpleGraph.card_interedges_le_mul" |
| ], |
| "bm25": [ |
| "SimpleGraph.zarankiewicz_le_iff", |
| "SimpleGraph.lt_zarankiewicz_iff_of_nonneg", |
| "SimpleGraph.zarankiewicz_of_fintypeCard_eq", |
| "SimpleGraph.lt_zarankiewicz_iff", |
| "SimpleGraph.extremalNumber_le_iff_of_nonneg", |
| "SimpleGraph.farFromTriangleFree_iff", |
| "SimpleGraph.farFromTriangleFree.le_card_sub_card", |
| "SimpleGraph.zarankiewicz_le_extremalNumber", |
| "SimpleGraph.deleteFar_iff", |
| "SimpleGraph.extremalNumber_le_iff", |
| "SimpleGraph.two_mul_extremalNumber_le_zarankiewicz_symm", |
| "SimpleGraph.DeleteFar.le_card_sub_card", |
| "SimpleGraph.card_edgeFinset_sup_edge", |
| "SimpleGraph.isBipartiteWith_sum_degrees_eq_twice_card_edges", |
| "SimpleGraph.card_edgeFinset_of_isExtremal_free", |
| "SimpleGraph.CliqueFree.card_edgeFinset_le" |
| ], |
| "rrf_bm25_e5_instr": [ |
| "SimpleGraph.zarankiewicz_of_fintypeCard_eq", |
| "SimpleGraph.lt_zarankiewicz_iff_of_nonneg", |
| "SimpleGraph.zarankiewicz_le_iff", |
| "SimpleGraph.lt_zarankiewicz_iff", |
| "SimpleGraph.card_edgeFinset_sup_edge", |
| "SimpleGraph.card_edgeFinset_map", |
| "SimpleGraph.card_edgeFinset_of_isExtremal_free", |
| "SimpleGraph.extremalNumber_le_iff_of_nonneg", |
| "SimpleGraph.card_edgeFinset_le_extremalNumber", |
| "SimpleGraph.extremalNumber_le_iff", |
| "SimpleGraph.isBipartiteWith_sum_degrees_eq_twice_card_edges", |
| "SimpleGraph.CliqueFree.card_edgeFinset_le", |
| "SimpleGraph.zarankiewicz_le_extremalNumber", |
| "SimpleGraph.lt_extremalNumber_iff_of_nonneg", |
| "SimpleGraph.deleteFar_iff", |
| "SimpleGraph.IsSRGWith.of_adj" |
| ] |
| } |
| ] |
| } |
