{ "catalog_sha256_by_recorded_version": {}, "per_theorem": [ { "name": "zero_add", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0000" }, { "name": "add_succ_left", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0001" }, { "name": "add_comm", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0002" }, { "name": "add_assoc", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0003" }, { "name": "mul_zero_left", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0004" }, { "name": "mul_succ_left", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0005" }, { "name": "mul_comm", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0006" }, { "name": "mul_add", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0007" }, { "name": "mul_assoc", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0008" }, { "name": "one_mul", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0009" }, { "name": "mul_one", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT000A" }, { "name": "add_mul", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT000B" }, { "name": "succ_ne_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT000C" }, { "name": "succ_injective", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT000D" }, { "name": "le_refl", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT000E" }, { "name": "le_trans", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT000F" }, { "name": "no_succ_add_fixed", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT000G" }, { "name": "drop_add_prefix_from_fixed", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT000H" }, { "name": "antisymm_from_witnesses", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT000I" }, { "name": "le_antisymm", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT000J" }, { "name": "le_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT000K" }, { "name": "add_eq_zero_right", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT000L" }, { "name": "mul_eq_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT000M" }, { "name": "zero_or_succ", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT000Q" }, { "name": "nonzero_is_succ", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT000R" }, { "name": "add_congr", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT000S" }, { "name": "mul_congr", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT000T" }, { "name": "add_right_cancel", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT000U" }, { "name": "add_left_cancel", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT000V" }, { "name": "zero_le", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT000W" }, { "name": "le_succ_self", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT000X" }, { "name": "le_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT000Y" }, { "name": "one_le_of_ne_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0010" }, { "name": "ne_zero_of_one_le", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0011" }, { "name": "le_add_left", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0012" }, { "name": "le_add_right", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0013" }, { "name": "add_le_add_right", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0014" }, { "name": "add_le_add_left", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0015" }, { "name": "succ_le_succ", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0016" }, { "name": "le_of_succ_le_succ", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0017" }, { "name": "le_succ", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0018" }, { "name": "lt_to_le", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0019" }, { "name": "lt_irrefl_expanded", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT001B" }, { "name": "le_eq_or_lt", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT001C" }, { "name": "lt_of_lt_of_le", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT001D" }, { "name": "lt_of_le_of_lt", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT001E" }, { "name": "lt_trans", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT001F" }, { "name": "le_or_lt", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT001G" }, { "name": "lt_trichotomy", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT001H" }, { "name": "lt_not_le", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT001I" }, { "name": "le_not_lt", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT001J" }, { "name": "lt_not_eq_add_middle", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT001K" }, { "name": "mul_le_mul_left", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT001L" }, { "name": "mul_le_mul_right", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT001M" }, { "name": "mul_lt_mul_succ_left_nonzero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT001N" }, { "name": "division_remainder_succ", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT001O" }, { "name": "division_remainder_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT001P" }, { "name": "division_block_upper", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT001R" }, { "name": "positive_quotient_gap_impossible", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT001S" }, { "name": "division_remainder_unique", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT001U" }, { "name": "zero_remainder_implies_multiple", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT001V" }, { "name": "multiple_has_zero_remainder", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT001W" }, { "name": "add_eq_zero_left", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT001X" }, { "name": "mul_eq_one_components", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0020" }, { "name": "mul_ne_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0021" }, { "name": "mul_left_cancel_nonzero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0022" }, { "name": "two_large_factors_impossible", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0024" }, { "name": "prime_two", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0025" }, { "name": "multiple_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0026" }, { "name": "one_multiple", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0027" }, { "name": "multiple_refl", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0028" }, { "name": "multiple_mul_right", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT002A" }, { "name": "multiple_mul_left", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT002B" }, { "name": "multiple_trans", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT002C" }, { "name": "divisor_le_nonzero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT002D" }, { "name": "divisor_one", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT002E" }, { "name": "multiple_antisymm", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT002F" }, { "name": "factor_difference", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT002G" }, { "name": "divides_remainder", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT002H" }, { "name": "divides_linear_step", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT002I" }, { "name": "is_gcd_zero_right", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT002L" }, { "name": "is_gcd_euclid_forward", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT002S" }, { "name": "gcd_exists_up_to", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT002U" }, { "name": "gcd_exists_relational", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT002V" }, { "name": "coprime_symm", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT002W" }, { "name": "coprime_one_right", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT002X" }, { "name": "coprime_one_left", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT002Y" }, { "name": "is_gcd_one_to_coprime", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0031" }, { "name": "add_permute_outer", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0032" }, { "name": "balanced_bezout_euclid_step", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0033" }, { "name": "gcd_balanced_bezout_exists_up_to", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0034" }, { "name": "gcd_balanced_bezout_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0035" }, { "name": "balanced_combination_scale_right", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0036" }, { "name": "common_divisor_divides_balanced_result", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0037" }, { "name": "coprime_balanced_bezout", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0038" }, { "name": "gauss_coprime_cancel", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0039" }, { "name": "eq_decidable", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT003A" }, { "name": "multiple_decidable_nonzero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT003B" }, { "name": "multiple_decidable", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT003C" }, { "name": "factor_property_succ", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT003D" }, { "name": "factor_search_up_to", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT003E" }, { "name": "prime_or_composite", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT003F" }, { "name": "prime_nonzero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT003G" }, { "name": "prime_decidable", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT003H" }, { "name": "proper_factor_lt", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT003J" }, { "name": "prime_divisor_exists_up_to", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT003K" }, { "name": "prime_divisor_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT003L" }, { "name": "prime_divisor_eq_one_or_self", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT003M" }, { "name": "euclid_prime_dvd_product", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT003N" }, { "name": "mod_eq_refl", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT003O" }, { "name": "mod_eq_trans", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT003Q" }, { "name": "mod_eq_add", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT003R" }, { "name": "mod_eq_mul_right", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT003S" }, { "name": "mod_eq_mul_left", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT003T" }, { "name": "mod_eq_bounded_unique", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT003W" }, { "name": "mod_eq_to_remainder_decomposition", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT003X" }, { "name": "beta_modulus_nonzero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT003Y" }, { "name": "beta_at_self_of_bound", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0040" }, { "name": "beta_at_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0041" }, { "name": "beta_at_unique", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0042" }, { "name": "beta_at_of_mod_eq_bound", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0045" }, { "name": "dvd_to_mod_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0046" }, { "name": "bezout_mod_left", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT004C" }, { "name": "bezout_mod_right", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT004D" }, { "name": "mod_eq_predecessor_cancel", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT004E" }, { "name": "binary_crt", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT004F" }, { "name": "beta_modulus_coprime_base", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT004I" }, { "name": "common_divisor_beta_moduli_divides_gap_times_c", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT004J" }, { "name": "beta_moduli_coprime_of_gap_dvd", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT004K" }, { "name": "bounded_common_multiple_step", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT004M" }, { "name": "bounded_common_multiple_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT004N" }, { "name": "beta_moduli_coprime_of_lt_bounded_common_multiple", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT004O" }, { "name": "beta_moduli_pairwise_coprime_bounded", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT004P" }, { "name": "coprime_mul_left", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT004R" }, { "name": "coprime_mul_right", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT004S" }, { "name": "mod_eq_of_mod_eq_multiple", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT004T" }, { "name": "binary_crt_fold_step", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT004U" }, { "name": "right_factor_divides_product", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT004V" }, { "name": "beta_value_le_code", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0053" }, { "name": "base_le_beta_modulus", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0054" }, { "name": "le_scaled_nonzero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0055" }, { "name": "scaled_bounded_common_multiple", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0056" }, { "name": "beta_value_lt_scaled_base", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0057" }, { "name": "new_value_lt_scaled_base", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0058" }, { "name": "beta_exclusive_accumulated_product_step", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0059" }, { "name": "beta_exclusive_recode_congruence_step", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT005A" }, { "name": "beta_exclusive_recode_invariant_step", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT005B" }, { "name": "bounded_beta_exclusive_recode_invariant", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT005C" }, { "name": "beta_prefix_extend", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT005D" }, { "name": "beta_prefix_product_trace_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT005E" }, { "name": "beta_product_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT005F" }, { "name": "beta_product_functional", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT005G" }, { "name": "beta_product_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT005I" }, { "name": "beta_product_succ_decompose", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT005J" }, { "name": "beta_product_succ_append", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT005K" }, { "name": "beta_product_transport_prefix", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT005L" }, { "name": "beta_factor_divides_product", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0069" }, { "name": "prime_three", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT006N" }, { "name": "parity_cases", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0072" }, { "name": "beta_repeat_empty", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT007U" }, { "name": "beta_repeat_succ_extend", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT007V" }, { "name": "beta_repeat_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT007W" }, { "name": "beta_repeat_entry_eq", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT007X" }, { "name": "beta_repeat_transport_entry", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT007Y" }, { "name": "pow_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0080" }, { "name": "pow_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0081" }, { "name": "pow_functional", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0082" }, { "name": "pow_successor_decompose", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0083" }, { "name": "beta_range_empty", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0084" }, { "name": "beta_range_succ_extend", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0085" }, { "name": "beta_range_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0086" }, { "name": "beta_range_entry_eq", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0087" }, { "name": "beta_range_transport_entry", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0088" }, { "name": "beta_prefix_sum_trace_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0089" }, { "name": "beta_sum_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT008A" }, { "name": "beta_sum_trace_functional", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT008B" }, { "name": "beta_sum_functional", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT008C" }, { "name": "beta_sum_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT008E" }, { "name": "beta_sum_succ_decompose", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT008F" }, { "name": "all_bits_prefix_succ", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT008J" }, { "name": "all_bits_last_succ", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT008K" }, { "name": "bit_count_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT008L" }, { "name": "bit_count_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT008N" }, { "name": "bit_count_succ_decompose", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT008O" }, { "name": "bit_count_bounded", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT008P" }, { "name": "prime_coprime_or_divides", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT008Q" }, { "name": "prime_not_divides_coprime", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT008R" }, { "name": "distinct_primes_coprime", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT008S" }, { "name": "factorial_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT008Y" }, { "name": "factorial_functional", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0090" }, { "name": "factorial_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0091" }, { "name": "factorial_succ_decompose", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0092" }, { "name": "pow_one_from_zero_successor", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0093" }, { "name": "pow_one", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0094" }, { "name": "pow_successor_pair_mul", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0095" }, { "name": "lt_three_cases", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT0097" }, { "name": "pow_two_from_one_successor", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT009V" }, { "name": "pow_two", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT009W" }, { "name": "pow_add", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT009X" }, { "name": "finite_lt_succ_eq_or_lt", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT00AA" }, { "name": "prime_is_succ_succ", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT00AW" }, { "name": "coprime_product_is_lcm", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "stable_closed", "checked_use": true, "evidence_status": "stable_closed", "stable_member": true }, "recorded_first_version": "not_recorded", "tag": "BT00BG" }, { "name": "beta_product_pointwise_coprime", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00DH" }, { "name": "beta_sum_transport_prefix", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00I9" }, { "name": "eisenstein_initial_segment_prefix_all_bits", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00JA" }, { "name": "eisenstein_initial_segment_decoded_choice", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00JB" }, { "name": "beta_all_one_bit_count_exact", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00JC" }, { "name": "eisenstein_initial_segment_bit_count_functional", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00JD" }, { "name": "eisenstein_initial_segment_bit_count_exact", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00JE" }, { "name": "beta_sum_pointwise_add", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00K5" }, { "name": "add_shuffle_middle", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00MY" }, { "name": "prime_strictly_above_decidable", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00PR" }, { "name": "bounded_prime_interval_search", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00PS" }, { "name": "mul_le_mul", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00PV" }, { "name": "le_mul_of_one_le_right", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00PW" }, { "name": "le_mul_of_one_le_left", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00PX" }, { "name": "pow_base_monotone", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00PY" }, { "name": "one_le_pow", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00Q0" }, { "name": "pow_nonzero_of_one_le", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00Q1" }, { "name": "power_divides_decidable", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00Q3" }, { "name": "power_divides_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00Q4" }, { "name": "bounded_power_valuation_search", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00Q5" }, { "name": "bounded_power_valuation_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00Q6" }, { "name": "power_valuation_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00Q7" }, { "name": "power_valuation_functional", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00Q8" }, { "name": "power_valuation_power_divides", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00Q9" }, { "name": "power_valuation_dominates", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00QA" }, { "name": "prime_two_le", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00QD" }, { "name": "succ_le_mul_of_two_le_right", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00QE" }, { "name": "prime_power_exponent_le", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00QF" }, { "name": "prime_power_divides_exponent_le_value", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00QG" }, { "name": "power_valuation_successor_not_divides", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00QH" }, { "name": "power_valuation_selected_and_successor_not_divides", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00QI" }, { "name": "mul_shuffle_four", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00QJ" }, { "name": "power_divides_exponent_antitone", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00QK" }, { "name": "power_divides_add_mul", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00QL" }, { "name": "power_divides_successor_of_cofactor", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00QM" }, { "name": "prime_power_successor_cancel_cofactor", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00QN" }, { "name": "prime_nondivisor_mul", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00QO" }, { "name": "power_valuation_exact_cofactor", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00QP" }, { "name": "power_valuation_mul_successor_not_divides", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00QQ" }, { "name": "power_valuation_mul_lower", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00QR" }, { "name": "power_valuation_mul_upper", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00QS" }, { "name": "prime_power_valuation_mul", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00QT" }, { "name": "two_mul_eq_add_self", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00QU" }, { "name": "pow_mul_base", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00QV" }, { "name": "pow_two_base_two_value_four", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00QW" }, { "name": "ceil_div_six_shift", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00R0" }, { "name": "ceil_div_six_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00R1" }, { "name": "ceil_div_six_functional", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00R2" }, { "name": "square_six_shift_identity", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00R4" }, { "name": "ceil_div_six_square_six_step", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00R5" }, { "name": "floor_sqrt_lower_bound", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00R6" }, { "name": "floor_sqrt_strict_upper_bound", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00R7" }, { "name": "square_lt_successor_square", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00R9" }, { "name": "floor_sqrt_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00RA" }, { "name": "floor_sqrt_monotone", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00RC" }, { "name": "mul_le_cancel_left_nonzero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00RD" }, { "name": "three_mul_eq_two_mul_add_self", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00RE" }, { "name": "ceil_div_six_le_of_upper", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00RF" }, { "name": "double_triple_remainder_complement_budget", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00RG" }, { "name": "canonical_double_triple_remainder_complement_budget", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00RH" }, { "name": "floor_ceil_complement_budget", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00RI" }, { "name": "floor_ceil_division_budget", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00RJ" }, { "name": "factorial_nonzero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00RK" }, { "name": "prime_power_valuation_one_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00RL" }, { "name": "factorial_valuation_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00RM" }, { "name": "prime_factorial_valuation_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00RO" }, { "name": "prime_factorial_valuation_succ", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00RP" }, { "name": "prime_power_quotient_prefix_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00S0" }, { "name": "power_quotient_prefix_transport", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00S1" }, { "name": "prime_legendre_sum_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00S2" }, { "name": "legendre_sum_functional", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00S3" }, { "name": "legendre_sum_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00S4" }, { "name": "pow_successor_compose", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00S5" }, { "name": "prime_power_quotient_tail_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00SA" }, { "name": "prime_power_divides_exponent_le_valuation", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00SB" }, { "name": "power_divides_of_exponent_le_valuation", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00SC" }, { "name": "eisenstein_initial_segment_indicator_choice", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00SD" }, { "name": "eisenstein_initial_segment_prefix_extend", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00SE" }, { "name": "eisenstein_initial_segment_prefix_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00SF" }, { "name": "division_remainder_successor_cases", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00SG" }, { "name": "division_successor_quotient_by_bit", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00SH" }, { "name": "valuation_threshold_bit_decides_power_divides", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00SI" }, { "name": "power_quotient_prefix_decoded_divrem", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00SJ" }, { "name": "power_quotient_successor_pointwise_add", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00SK" }, { "name": "pow_successor_compose_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00SL" }, { "name": "pow_mul_exp_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00SM" }, { "name": "pow_exponent_monotone_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00SN" }, { "name": "pow_two_seed_bundle_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00SO" }, { "name": "beta_sum_succ_last_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00SR" }, { "name": "prime_power_quotient_prefix_last_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00SS" }, { "name": "legendre_sum_zero_extended_prefix", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00ST" }, { "name": "initial_segment_prefix_sum_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00SU" }, { "name": "prime_legendre_sum_succ", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00SV" }, { "name": "bertrand_h_six_step_transport_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00SW" }, { "name": "bertrand_j_six_step_transport_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00SX" }, { "name": "bertrand_hj_six_step_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00SY" }, { "name": "factorial_legendre_successor_agreement", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00T0" }, { "name": "prime_factorial_valuation_eq_legendre_sum", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00T1" }, { "name": "beta_pascal_zero_row_extend", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00T2" }, { "name": "beta_pascal_zero_row_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00T3" }, { "name": "beta_pascal_row_step_extend", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00T4" }, { "name": "beta_pascal_row_step_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00T5" }, { "name": "beta_pascal_table_prefix_extend", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00T6" }, { "name": "beta_pascal_table_prefix_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00T7" }, { "name": "choose_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00T8" }, { "name": "beta_pascal_zero_row_pointwise_functional", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00T9" }, { "name": "beta_pascal_row_step_pointwise_functional", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TA" }, { "name": "beta_pascal_table_row_pointwise_functional", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TB" }, { "name": "choose_functional", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TC" }, { "name": "choose_out_of_range_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TD" }, { "name": "choose_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TE" }, { "name": "beta_pascal_table_diagonal_boundary", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TF" }, { "name": "choose_self", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TG" }, { "name": "beta_pascal_table_successor_cell_recurrence", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TH" }, { "name": "choose_succ_succ_of_lt", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TI" }, { "name": "choose_succ_succ", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TJ" }, { "name": "choose_self_of_eq", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TK" }, { "name": "choose_symmetry", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TL" }, { "name": "choose_positive", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TM" }, { "name": "central_binom_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TN" }, { "name": "central_binom_positive", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TP" }, { "name": "central_binom_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TQ" }, { "name": "choose_upper_eq_transport", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TR" }, { "name": "central_binom_succ_double_middle", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TS" }, { "name": "choose_weighted_vertical", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TT" }, { "name": "central_binom_succ_recurrence", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TU" }, { "name": "factorial_length_eq_transport", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TV" }, { "name": "factorial_weighted_product_combine", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TW" }, { "name": "choose_factorial_bridge", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TX" }, { "name": "mul_lt_mul_right_nonzero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00TY" }, { "name": "four_power_central_recurrence_step", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00U0" }, { "name": "pow_four_four_exact", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00U1" }, { "name": "central_binom_four_weighted_of_recurrence", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00U2" }, { "name": "four_pow_central_seed_package", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00U3" }, { "name": "four_pow_lt_mul_central_binom", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00U4" }, { "name": "primorial_factor_choice_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00U5" }, { "name": "primorial_factor_choice_functional", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00U6" }, { "name": "primorial_factor_prefix_extend", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00U7" }, { "name": "primorial_factor_prefix_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00U8" }, { "name": "primorial_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00UA" }, { "name": "primorial_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00UC" }, { "name": "primorial_succ_decompose", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00UD" }, { "name": "primorial_positive", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00UE" }, { "name": "primorial_index_eq_transport", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00UF" }, { "name": "beta_product_prefix_suffix_split", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00UQ" }, { "name": "primorial_interval_factor_prefix_extend", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00UR" }, { "name": "primorial_interval_factor_prefix_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00US" }, { "name": "primorial_interval_factor_prefix_shift", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00UW" }, { "name": "primorial_factor_prefix_restrict_add", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00UX" }, { "name": "primorial_prefix_interval_split", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00UY" }, { "name": "factorial_prime_divides_of_le", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VA" }, { "name": "factorial_prime_le_of_divides", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VB" }, { "name": "choose_prime_divides_between", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VC" }, { "name": "beta_pairwise_coprime_product_divides_common_multiple", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VD" }, { "name": "primorial_interval_pairwise_coprime", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VE" }, { "name": "primorial_interval_divides_choose_between", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VF" }, { "name": "primorial_even_interval_divides_central", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VG" }, { "name": "primorial_odd_interval_divides_middle", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VH" }, { "name": "primorial_even_interval_le_central", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VI" }, { "name": "primorial_odd_interval_le_middle", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VJ" }, { "name": "central_binom_strong_upper_step", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VK" }, { "name": "central_binom_recurrence_double_bundle", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VL" }, { "name": "central_binom_strong_upper_of_laws", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VM" }, { "name": "central_binom_upper_support_package", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VN" }, { "name": "central_binom_strong_upper", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VO" }, { "name": "central_binom_odd_middle_le_four_pow", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VP" }, { "name": "primorial_one", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VQ" }, { "name": "double_half_predecessor_data", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VR" }, { "name": "odd_positive_prefix_predecessor_bound", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VS" }, { "name": "central_binom_nonzero_strong_upper", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VT" }, { "name": "primorial_four_power_support_package", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VU" }, { "name": "primorial_le_four_pow_bounded", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VV" }, { "name": "primorial_le_four_pow", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VW" }, { "name": "central_binom_prime_divisor_le_double", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VX" }, { "name": "no_bertrand_central_prime_divisor_le", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00VY" }, { "name": "power_valuation_nonzero_exponent_divides_base", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00W0" }, { "name": "no_bertrand_central_prime_divisor_ranges", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00W2" }, { "name": "pow_block_bound_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00W3" }, { "name": "pow_three_five_le_pow_four_four_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00W4" }, { "name": "pow_eleven_two_le_pow_two_seven_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00W5" }, { "name": "pow_six_ten_le_pow_four_thirteen_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00W6" }, { "name": "linear_square_budget", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00W7" }, { "name": "bertrand_scaled_budget_root_32", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00W8" }, { "name": "bertrand_scaled_budget_root_33", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00W9" }, { "name": "bertrand_scaled_budget_root_34", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WA" }, { "name": "bertrand_scaled_budget_root_35", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WB" }, { "name": "bertrand_scaled_budget_root_36", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WC" }, { "name": "bertrand_scaled_budget_root_37", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WD" }, { "name": "ceil_div_six_budget_of_scaled_le", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WE" }, { "name": "pow_six_six_le_pow_four_eight_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WF" }, { "name": "pow_six_four_le_pow_four_six_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WG" }, { "name": "pow_three_five_block_plus_one_le_pow_four_four_block_plus_one_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WH" }, { "name": "pow_two_double_eq_pow_four_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WI" }, { "name": "pow_two_successor_double_le_pow_four_successor_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WJ" }, { "name": "pow_eleven_double_block_le_pow_two_seven_block_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WK" }, { "name": "pow_eleven_double_block_le_pow_four_even_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WL" }, { "name": "pow_eleven_double_block_le_pow_four_odd_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WM" }, { "name": "pow_six_ten_block_le_pow_four_thirteen_block_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WN" }, { "name": "pow_thirty_six_double_block_eq_pow_six_four_block_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WO" }, { "name": "bertrand_h_root_32_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WP" }, { "name": "bertrand_h_root_33_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WQ" }, { "name": "bertrand_h_root_34_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WR" }, { "name": "bertrand_h_root_35_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WS" }, { "name": "bertrand_h_root_36_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WT" }, { "name": "bertrand_h_root_37_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WU" }, { "name": "bertrand_j_base_thirty_two_window_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WV" }, { "name": "bertrand_hj_base_window_thirty_two_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WW" }, { "name": "scaled_factor_square_identity", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WX" }, { "name": "thirty_two_square_eq_twice_sixteen_times_thirty_two", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00WY" }, { "name": "floor_sqrt_factorized_threshold_thirty_two", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00X0" }, { "name": "six_block_window_decomposition_above_thirty_two", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00X1" }, { "name": "bertrand_hj_six_block_iterate_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00X2" }, { "name": "bertrand_hj_envelope_thirty_two", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00X3" }, { "name": "bertrand_floor_power_product_le_h_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00X4" }, { "name": "bertrand_four_power_product_le_of_sum_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00X5" }, { "name": "bertrand_main_inequality_factorized_from_total", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00X6" }, { "name": "bertrand_main_inequality_factorized", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00X7" }, { "name": "bertrand_main_inequality_nat", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00X8" }, { "name": "beta_product_pointwise_le", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00X9" }, { "name": "beta_product_uniform_le_pow", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00XA" }, { "name": "add_lt_add", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00XB" }, { "name": "add_lt_cancel_left", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00XC" }, { "name": "division_zero_quotient_of_lt", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00XF" }, { "name": "division_double_quotient_bit", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00XG" }, { "name": "pow_le_pow_of_exponent_le", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00XJ" }, { "name": "pow_tail_strict_of_square", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00XK" }, { "name": "power_valuation_value_eq_transport", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00XL" }, { "name": "central_binom_factorial_valuation_balance", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00XM" }, { "name": "central_binom_legendre_valuation_balance", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00XN" }, { "name": "prime_power_quotient_zero_of_exponent_gt", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00XO" }, { "name": "power_quotient_prefix_tail_entry_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00XP" }, { "name": "power_quotient_prefix_sum_extend_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00XQ" }, { "name": "legendre_sum_extended_prefix_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00XR" }, { "name": "double_quotient_carry_choice", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00XV" }, { "name": "double_quotient_carry_prefix_extend", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00XW" }, { "name": "double_quotient_carry_prefix_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00XX" }, { "name": "double_quotient_carry_prefix_all_bits", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00XY" }, { "name": "double_quotient_carry_prefix_restrict", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00Y0" }, { "name": "bit_count_positive_last_one", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00Y1" }, { "name": "division_successor_quotient_divisor_le", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00Y2" }, { "name": "beta_sum_double_carry_exact", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00Y3" }, { "name": "central_binom_carry_bit_count", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00Y4" }, { "name": "central_binom_prime_power_contribution_le_double", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00Y5" }, { "name": "central_binom_prime_square_tail_exponent_not_two_le", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00Y6" }, { "name": "central_binom_prime_square_tail_valuation_le_one", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00Y7" }, { "name": "division_quotient_one_of_bounds", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00Y8" }, { "name": "division_quotient_two_of_bounds", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00Y9" }, { "name": "prime_square_tail_of_two_three_range", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YA" }, { "name": "division_first_two_of_two_three_range", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YB" }, { "name": "double_quotient_carry_prefix_entries_zero", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YC" }, { "name": "central_binom_prime_valuation_zero_of_exact_double_quotients", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YD" }, { "name": "central_binom_prime_valuation_zero_two_thirds_range", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YE" }, { "name": "division_three_scaled_upper_of_quotient_lt", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YF" }, { "name": "central_binom_prime_valuation_zero_above_third_quotient", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YG" }, { "name": "floor_sqrt_above_root_power_two_strict", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YH" }, { "name": "central_binom_prime_above_floor_sqrt_valuation_le_one", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YI" }, { "name": "no_bertrand_central_nonzero_valuation_live_ranges", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YJ" }, { "name": "no_bertrand_central_nonzero_valuation_factor_ranges", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YK" }, { "name": "no_bertrand_central_nonzero_contribution_factor_ranges", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YL" }, { "name": "no_bertrand_central_prime_contribution_ranges", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YM" }, { "name": "prime_contribution_choice_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YN" }, { "name": "prime_contribution_choice_functional", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YO" }, { "name": "prime_contribution_prefix_extend", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YP" }, { "name": "prime_contribution_prefix_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YQ" }, { "name": "prime_contribution_product_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YS" }, { "name": "coprime_power_right", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YU" }, { "name": "coprime_powers", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YV" }, { "name": "prime_contribution_prefix_pairwise_coprime", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YW" }, { "name": "prime_contribution_factor_divides", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YX" }, { "name": "prime_contribution_product_divides", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT00YY" }, { "name": "prime_contribution_selected_entry", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT0100" }, { "name": "prime_contribution_selected_successor_divides", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT0101" }, { "name": "prime_contribution_cofactor_prime_contradiction", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT0102" }, { "name": "prime_contribution_cofactor_eq_one", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT0103" }, { "name": "prime_contribution_reverse_divides", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT0104" }, { "name": "prime_contribution_product_eq", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT0105" }, { "name": "prime_contribution_complete_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT0106" }, { "name": "central_binom_prime_contribution_product_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT0107" }, { "name": "no_bertrand_central_contribution_choice_ranges", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT0108" }, { "name": "two_lt_double_lower_six", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT010A" }, { "name": "floor_sqrt_two_le_of_two_lt", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT010B" }, { "name": "three_mul_le_square_of_three_le", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT010C" }, { "name": "floor_sqrt_three_mul_le_double", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT010D" }, { "name": "division_quotient_lower_of_scaled_le", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT010E" }, { "name": "floor_sqrt_le_third_quotient", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT010F" }, { "name": "floor_sqrt_third_quotient_gap_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT010G" }, { "name": "division_quotient_le_dividend", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT010H" }, { "name": "third_quotient_double_gap_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT010I" }, { "name": "floor_third_double_gap_package", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT010J" }, { "name": "prime_contribution_interval_prefix_extend", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT010K" }, { "name": "prime_contribution_interval_prefix_exists", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT010L" }, { "name": "prime_contribution_interval_prefix_shift", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT010P" }, { "name": "prime_contribution_prefix_restrict_add", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT010Q" }, { "name": "prime_contribution_prefix_interval_split", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT010R" }, { "name": "prime_contribution_product_length_eq_transport", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT010S" }, { "name": "beta_product_all_one_exact", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT010U" }, { "name": "no_bertrand_small_contribution_choice_le_double", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT010V" }, { "name": "no_bertrand_middle_contribution_choice_le_selector", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT010W" }, { "name": "no_bertrand_high_contribution_choice_eq_one", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT010X" }, { "name": "no_bertrand_small_contribution_product_le_power", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT010Y" }, { "name": "no_bertrand_middle_contribution_interval_le_primorial_interval", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT0110" }, { "name": "no_bertrand_middle_contribution_interval_le_four_pow", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT0111" }, { "name": "no_bertrand_high_contribution_interval_eq_one", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT0112" }, { "name": "central_binom_factorization_small", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT0113" }, { "name": "central_binom_le_of_no_bertrand_prime", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT0114" }, { "name": "bertrand_eventually_closed_upper", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT0115" }, { "name": "fixed_nontrivial_factor_not_prime", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT0116" }, { "name": "factor_pair_has_small_member_below_square", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT0117" }, { "name": "nonprime_has_small_prime_divisor_below_square", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT0118" }, { "name": "prime_of_no_small_prime_divisor_below_square", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT0119" }, { "name": "prime_le_twenty_two_cases", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT011A" }, { "name": "nonzero_remainder_not_multiple", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT011B" }, { "name": "scaled_remainder_lift", "recorded_authority": { "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "evidence_status": "alpha_closed", "stable_member": false }, "recorded_first_version": "not_recorded", "tag": "BT011C" }, { "name": "double_scaled_remainder_lift", 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