{ "catalog_sha256_by_recorded_version": { "v27": "481a9a378e54dc389422819587e8377a07b63a0d5d50286ffdfd28f0c4bdb2e6" }, "per_theorem": [ { "name": "matrix_recursive_node_code_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0001" }, { "name": "matrix_recursive_prefix_refl", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0002" }, { "name": "matrix_recursive_prefix_trans", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, 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"alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0013" }, { "name": "matrix_recursive_node_code_injective", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0014" }, { "name": "matrix_recursive_record_injective", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0015" }, { "name": "matrix_recursive_history_step_at", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0016" }, { "name": "signed_recursive_determinant_zero_value", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0017" }, { "name": "signed_recursive_determinant_successor_decomposition", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0018" }, { "name": "matrix_recursive_lt_add_left", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0019" }, { "name": "matrix_recursive_flattened_index_bound", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL001A" }, { "name": "matrix_recursive_quotient_row_bound", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL001B" }, { "name": "matrix_recursive_minor_cell_transport", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL001C" }, { "name": "matrix_recursive_minor_prefix_transport", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL001D" }, { "name": "matrix_recursive_minor_prefix_functional", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL001E" }, { "name": "matrix_recursive_signed_minor_extensional", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL001F" }, { "name": "matrix_recursive_alternating_prefix_transport", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0020" }, { "name": "matrix_recursive_alternating_fold_transport", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0021" }, { "name": "matrix_recursive_alternating_fold_extensional", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0022" }, { "name": "matrix_recursive_matrix_equality_refl", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0023" }, { "name": "matrix_recursive_initial_row_prefix", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0024" }, { "name": "matrix_recursive_cofactor_streams_from_functionality", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0025" }, { "name": "matrix_recursive_determinant_extensional", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0026" }, { "name": "signed_recursive_determinant_functional", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0027" }, { "name": "signed_recursive_determinant_exists_unique", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0028" }, { "name": "signed_recursive_determinant_from_evaluated_cofactors", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0029" }, { "name": "signed_recursive_determinant_cofactor_equation", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL002A" }, { "name": "signed_recursive_determinant_empty", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL002B" }, { "name": "signed_recursive_determinant_empty_equation", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL002C" }, { "name": "matrix_rank_bounded_prefix_value", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL002D" }, { "name": "matrix_rank_common_multiple_divides", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL002E" }, { "name": "matrix_rank_beta_moduli_common_multiple", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL002F" }, { "name": "matrix_rank_recode_congruences_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0030" }, { "name": "matrix_rank_bounded_recode_in_fixed_box", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0031" }, { "name": "matrix_rank_uniform_beta_prefix_box_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0032" }, { "name": "matrix_rank_no_index_below_zero", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0033" }, { "name": "matrix_rank_prefix_equality_symmetric", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0034" }, { "name": "matrix_rank_bounded_prefix_transport", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0035" }, { "name": "matrix_rank_injective_prefix_transport", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0036" }, { "name": "matrix_rank_injective_prefix_decidable", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0037" }, { "name": "matrix_rank_bounded_prefix_empty", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0038" }, { "name": "matrix_rank_bounded_prefix_drop_last", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0039" }, { "name": "matrix_rank_bounded_prefix_extend", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL003A" }, { "name": "matrix_rank_bounded_prefix_decidable", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL003B" }, { "name": "matrix_rank_selector_transport", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL003C" }, { "name": "matrix_rank_selector_decidable", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL003D" }, { "name": "matrix_rank_selector_dimension_bound", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL003E" }, { "name": "matrix_rank_selector_empty", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL003F" }, { "name": "matrix_rank_selected_point_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0040" }, { "name": "matrix_rank_selected_point_functional", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0041" }, { "name": "matrix_rank_selected_prefix_empty", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0042" }, { "name": "matrix_rank_selected_prefix_extend", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0043" }, { "name": "matrix_rank_selected_prefix_exists_nonzero", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0044" }, { "name": "matrix_rank_selected_square_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0045" }, { "name": "matrix_rank_signed_selected_square_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0046" }, { "name": "matrix_rank_selected_prefix_functional", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0047" }, { "name": "matrix_rank_signed_selected_square_functional", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0048" }, { "name": "matrix_rank_selected_determinant_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0049" }, { "name": "matrix_rank_selected_determinant_functional", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL004A" }, { "name": "matrix_rank_selected_point_selector_transport", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL004B" }, { "name": "matrix_rank_selected_prefix_selector_transport", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL004C" }, { "name": "matrix_rank_signed_selected_selector_transport", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL004D" }, { "name": "matrix_rank_selected_determinant_selector_transport", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL004E" }, { "name": "matrix_rank_selected_nonzero_value_decidable", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL004F" }, { "name": "matrix_rank_nonzero_selected_minor_decidable", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0050" }, { "name": "matrix_rank_nonzero_selected_minor_transport", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0051" }, { "name": "matrix_rank_selected_determinant_empty", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0052" }, { "name": "matrix_rank_nonzero_minor_dimension_bounds", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0053" }, { "name": "matrix_rank_nonzero_minor_empty", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0054" }, { "name": "matrix_rank_selected_column_search_decidable", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0055" }, { "name": "matrix_rank_selected_box_search_decidable", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0056" }, { "name": "matrix_rank_nonzero_minor_recode_in_box", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0057" }, { "name": "matrix_rank_nonzero_minor_of_box_search", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0058" }, { "name": "matrix_rank_nonzero_minor_decidable", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0059" }, { "name": "matrix_rank_le_successor_cases", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL005A" }, { "name": "matrix_rank_maximal_nonzero_prefix_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL005B" }, { "name": "matrix_rank_all_minors_zero_from_absence", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL005C" }, { "name": "matrix_rank_absence_from_all_minors_zero", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL005D" }, { "name": "rectangular_matrix_rank_certificate_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL005E" }, { "name": "rectangular_matrix_rank_functional", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL005F" }, { "name": "rectangular_matrix_rank_exists_unique", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0060" }, { "name": "rectangular_matrix_rank_successor_minors_zero", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0061" }, { "name": "rectangular_matrix_rank_zero_rows", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0062" }, { "name": "rectangular_matrix_rank_zero_columns", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0063" }, { "name": "integer_span_dot_product_pointwise_add", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0064" }, { "name": "integer_span_natural_cell_add_right", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0065" }, { "name": "integer_span_natural_product_entry", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0066" }, { "name": "integer_span_natural_product_add_right", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0067" }, { "name": "integer_span_pointwise_add_interchange", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0068" }, { "name": "integer_span_signed_product_negate", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0069" }, { "name": "integer_span_signed_product_equal_coefficients", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL006A" }, { "name": "integer_span_signed_product_add_right", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL006B" }, { "name": "integer_span_pair_equal_transitive", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL006C" }, { "name": "integer_span_pair_add_congruence", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL006D" }, { "name": "integer_vector_equal_reflexive", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL006E" }, { "name": "integer_vector_equal_transitive", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL006F" }, { "name": "integer_vector_equal_negated", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0070" }, { "name": "integer_vector_equal_components_zero", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0071" }, { "name": "integer_vector_equal_zero_from_same_components", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0072" }, { "name": "integer_vector_add_from_component_sums", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0073" }, { "name": "integer_vector_add_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0074" }, { "name": "integer_vector_add_transport_inputs", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0075" }, { "name": "integer_vector_add_functional", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0076" }, { "name": "integer_matrix_vector_product_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0077" }, { "name": "integer_matrix_vector_product_transport", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0078" }, { "name": "integer_matrix_vector_product_zero", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0079" }, { "name": "integer_matrix_vector_product_negated", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL007A" }, { "name": "integer_matrix_vector_add_coefficients", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL007B" }, { "name": "integer_matrix_vector_add_constructive", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL007C" }, { "name": "integer_column_span_transport", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL007D" }, { "name": "integer_column_span_zero", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL007E" }, { "name": "integer_column_span_contains_zero", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL007F" }, { "name": "integer_column_span_negated", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0080" }, { "name": "integer_column_span_negate_closed", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0081" }, { "name": "integer_column_span_add_closed", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0082" }, { "name": "integer_column_span_add_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0083" }, { "name": "integer_column_span_negate_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0084" }, { "name": "matrix_integer_vector_equality_restrict", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0085" }, { "name": "matrix_integer_vector_equality_symmetric", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0086" }, { "name": "matrix_integer_pair_product_balance", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0087" }, { "name": "matrix_integer_pair_negation_balance", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v27", "tag": "DL0088" }, { "name": "matrix_integer_cofactor_term_balance", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, 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