Step-by-step derivation
S001 · implies
Before
source roles = [qf-finite-event-cardinality, no-domain-field, no-operation-field, no-form-field]
After
derived = [[cardinality_NUMBER_not_probability]]
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 = [S original sample, [37, 38, 39]]
After
derived = [[37, 38, 39]]
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 = [E original event candidate, [37, 39]]
After
derived = [[37, 39]]
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, 37, [37, 38, 39]]
After
derived = [Yes]
Conditions: none
Check EACH candidate event element in ORIGINAL S.The empty event satisfies the subset condition vacuously.F=P(S)is not a probability law and does not imply equal likelihood.
Step identifiers and dependencies
Rule: Event_EACH_candidate_element_membership_in_ORIGINAL_S · Uses: G001, S003
S005 · implies
Before
source roles = [1, 39, [37, 38, 39]]
After
derived = [Yes]
Conditions: none
Check EACH candidate event element in ORIGINAL S.The empty event satisfies the subset condition vacuously.F=P(S)is not a probability law and does not imply equal likelihood.
Step identifiers and dependencies
Rule: Event_EACH_candidate_element_membership_in_ORIGINAL_S · Uses: G001, S004
S006 · implies
Before
source roles = [[37, 38, 39], [37, 39], P(S)]
After
derived = [[Yes, Yes], [], Yes]
Conditions: none
With EXACT F=P(S),event qualification is precisely E⊆S.An outside E is a LEGAL No in subset-validity;do not delete the witness first.Cardinality,occurrence and probability are distinct questions.
Step identifiers and dependencies
Rule: Event_FULLpowerset_qualification_ALL_subset_flags_NOT_probability · Uses: G001, S005
S007 · calculation
Before
Event cardinality ORIGINAL distinct element slot0 := sum(0, 1)
After
Event cardinality ORIGINAL distinct element slot0 = 1
Conditions: none
Use ORIGINAL operands and declared order for exact integer/rational arithmetic,not floats.Bounds are family-specific:do not revalidate derived values as RAW inputs or add blanket SAFE/n64 caps to BASE families.
Step identifiers and dependencies
Rule: exact_rational_arithmetic · Uses: G001, S006
S008 · calculation
Before
Event cardinality ORIGINAL distinct element slot1 := sum(1, 1)
After
Event cardinality ORIGINAL distinct element slot1 = 2
Conditions: none
Use ORIGINAL operands and declared order for exact integer/rational arithmetic,not floats.Bounds are family-specific:do not revalidate derived values as RAW inputs or add blanket SAFE/n64 caps to BASE families.
Step identifiers and dependencies
Rule: exact_rational_arithmetic · Uses: G001, S007
S009 · implies
Before
source roles = [[37, 38, 39], [37, 39]]
After
derived = [2]
Conditions: none
Count EACH distinct element for|E|.The answer is a NUMBER,not a fraction or probability.The empty event has cardinality0,even when S is empty.No uniform distribution is assumed.
Step identifiers and dependencies
Rule: Event_CARDINALITY_NUMBER_distinct_count_NO_probability_or_nonempty_S · Uses: G001, S008