Step-by-step derivation
S001 · implies
Before
source roles = [qf-finite-relative-complement, no-domain-field, no-operation-field, no-form-field]
After
derived = [[numeric_sorted_set_STRING_or_empty_symbol]]
Conditions: none
Check THIS bank interface:BASE equations use form/domain;BASE events/complement have no operation;factorials have no domain.ext18 uses local hyphens,other legacy operations underscores.Do not force every answer into a tuple or fraction.
Step identifiers and dependencies
Rule: R62_EXACT_source_keys_domain_operation_form_AND_output_types · Uses: G001
S002 · implies
Before
source roles = [U ORIGINAL explicit universe, [961, 962, 963, 964, 965]]
After
derived = [[961, 962, 963, 964, 965]]
Conditions: none
The BASE finite set is a DISTINCT integer list;do not silently repair duplicates.Sort numerically ONLY for derived display,retaining original data.Do not import the expectation100-element or SAFE bounds.
Step identifiers and dependencies
Rule: BASE_FINITE_set_distinct_INTEGER_list_no_silent_duplicate_fix · Uses: G001, S001
S003 · implies
Before
source roles = [A ORIGINAL subset, [961, 963]]
After
derived = [[961, 963]]
Conditions: none
The BASE finite set is a DISTINCT integer list;do not silently repair duplicates.Sort numerically ONLY for derived display,retaining original data.Do not import the expectation100-element or SAFE bounds.
Step identifiers and dependencies
Rule: BASE_FINITE_set_distinct_INTEGER_list_no_silent_duplicate_fix · Uses: G001, S002
S004 · implies
Before
source roles = [0, 961, [961, 963]]
After
derived = [No]
Conditions: none
For EACH ORIGINAL label of the EXPLICIT universe U,retain it ONLY when not in A.This is U\A,not A\U or complement in an unstated universe.
Step identifiers and dependencies
Rule: Complement_EACH_ORIGINAL_universe_label_NOT_in_A · Uses: G001, S003
S005 · implies
Before
source roles = [1, 962, [961, 963]]
After
derived = [Yes]
Conditions: none
For EACH ORIGINAL label of the EXPLICIT universe U,retain it ONLY when not in A.This is U\A,not A\U or complement in an unstated universe.
Step identifiers and dependencies
Rule: Complement_EACH_ORIGINAL_universe_label_NOT_in_A · Uses: G001, S004
S006 · implies
Before
source roles = [2, 963, [961, 963]]
After
derived = [No]
Conditions: none
For EACH ORIGINAL label of the EXPLICIT universe U,retain it ONLY when not in A.This is U\A,not A\U or complement in an unstated universe.
Step identifiers and dependencies
Rule: Complement_EACH_ORIGINAL_universe_label_NOT_in_A · Uses: G001, S005
S007 · implies
Before
source roles = [3, 964, [961, 963]]
After
derived = [Yes]
Conditions: none
For EACH ORIGINAL label of the EXPLICIT universe U,retain it ONLY when not in A.This is U\A,not A\U or complement in an unstated universe.
Step identifiers and dependencies
Rule: Complement_EACH_ORIGINAL_universe_label_NOT_in_A · Uses: G001, S006
S008 · implies
Before
source roles = [4, 965, [961, 963]]
After
derived = [Yes]
Conditions: none
For EACH ORIGINAL label of the EXPLICIT universe U,retain it ONLY when not in A.This is U\A,not A\U or complement in an unstated universe.
Step identifiers and dependencies
Rule: Complement_EACH_ORIGINAL_universe_label_NOT_in_A · Uses: G001, S007
S009 · implies
Before
source roles = [[961, 962, 963, 964, 965], [961, 963]]
After
derived = [[962, 964, 965], {962, 964, 965}, Yes]Conditions: none
AFTER A⊆U qualification,verify disjointness and union BACK to U,without lost/added labels.Display numeric increasing order once per element,or∅for empty.Keep ORIGINAL U/A order and data unchanged.
Step identifiers and dependencies
Rule: Complement_COMPLETE_disjoint_partition_of_fixed_U_numeric_set_display · Uses: G001, S008