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 = [[7, 8, 9], powerset(S)]
After
derived = [[7, 8, 9], 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(20, 5, 1)
After
Legacy probability ORIGINAL ALL numerator weights sum = 26
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 = [[7, 8, 9], [20, 5, 1], 26]
After
derived = [[[7, 20], [8, 5], [9, 1]], 26, 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 outcome7 running sum0 := sum(0, 20)
After
Legacy probability ORIGINAL included outcome7 running sum0 = 20
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 included outcome8 running sum1 := sum(20, 5)
After
Legacy probability ORIGINAL included outcome8 running sum1 = 25
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 · calculation
Before
Legacy probability ORIGINAL normalized event or complement fraction := div(25, 26)
After
Legacy probability ORIGINAL normalized event or complement fraction = 25/26
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, S006
S008 · implies
Before
source roles = [[7, 8, 9], [7, 8], [[7, 20], [8, 5], [9, 1]], 26]
After
derived = [25, [9], 25, 25/26]
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, S007