Step-by-step derivation
S001 · implies
Before
source roles = [qf-probability-weighted-event, weighted_event]
After
derived = [[reduced_probability_fraction_retaining_integer_denominator1]]
Conditions: none
List this scalar/label/set/point answer role or mode-specific ordered fields,not an imposed universal tuple.Retain legacy domain/underscore operation and integer fractions with/1;original bilingual snapshots stay unchanged.
Step identifiers and dependencies
Rule: source_answer_roles_or_ordered_fields_without_JS · Uses: G001
S002 · implies
Before
source roles = [[0, 1, 2], powerset(S)]
After
derived = [[0, 1, 2], 3]
Conditions: none
S is a nonempty set of at most100 distinct SAFE integers and F is explicitly the FULL powerset,not an event family inferred from one event.
Step identifiers and dependencies
Rule: Legacy_probability_NONEMPTY_S_FULLpowerset_exact_declared_event_family · Uses: G001, S001
S003 · calculation
Before
Legacy probability ORIGINAL ALL numerator weights sum := sum(13, 3, 0)
After
Legacy probability ORIGINAL ALL numerator weights sum = 16
Conditions: none
Substitute original roles exactly,without floating approximation or changed operands;extra teaching identities add no source-domain restrictions.
Step identifiers and dependencies
Rule: exact_rational_arithmetic · Uses: G001, S002
S004 · implies
Before
source roles = [[0, 1, 2], [13, 3, 0], 16]
After
derived = [[[0, 13], [1, 3], [2, 0]], 16, Yes, Yes, Yes, Yes]
Conditions: none
Bind weights to ORIGINAL raw S slots;set sorting does not change these associations.Validity needs a positive denominator,all nonnegative weights and the BigInt total equal to the denominator.A model-validity question may legally answerNo,without0/0,sign repair or renormalizing another model.
Step identifiers and dependencies
Rule: Legacy_probability_ORIGINAL_rawS_weight_alignment_and_model_qualification · Uses: G001, S003
S005 · calculation
Before
Legacy probability ORIGINAL included outcome0 running sum0 := sum(0, 13)
After
Legacy probability ORIGINAL included outcome0 running sum0 = 13
Conditions: none
Substitute original roles exactly,without floating approximation or changed operands;extra teaching identities add no source-domain restrictions.
Step identifiers and dependencies
Rule: exact_rational_arithmetic · Uses: G001, S004
S006 · calculation
Before
Legacy probability ORIGINAL normalized event or complement fraction := div(13, 16)
After
Legacy probability ORIGINAL normalized event or complement fraction = 13/16
Conditions: none
Substitute original roles exactly,without floating approximation or changed operands;extra teaching identities add no source-domain restrictions.
Step identifiers and dependencies
Rule: exact_rational_arithmetic · Uses: G001, S005
S007 · implies
Before
source roles = [[0, 1, 2], [0], [[0, 13], [1, 3], [2, 0]], 16]
After
derived = [13, [1, 2], 13, 13/16]
Conditions: none
On the full powerset define every event by its ORIGINAL weighted sum.Nonnegativity,total1 and regrouping disjoint events give finite(and countable,for finite S)additivity.A nonempty E can have mass0.The complement is in the SAME S;do not substitute sorted-slot weights or uniform counts.
Step identifiers and dependencies
Rule: Legacy_complete_finite_probability_axioms_and_same_carrier_complement · Uses: G001, S006