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R0070-35521 · q-20260914-basic-counting-principle-0001
A task can be completed through two explicitly disjoint branches with 2 and 3 outcomes. What is the total?
G001 — A task can be completed through two explicitly disjoint branches with 2 and 3 outcomes. What is the total?Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Before
source roles = [qf-basic-counting-principle, [branch_counts, conditional_stage_witness, mode, overlap_witness, stages]]
After
derived = [counting, null, null]
Conditions: none
Use THIS bank’s actual fields,operation/domain and types.BASE retains permissible extra metadata.Do not import LDL SAFE/set limits or a different bank’s deduplication rules.
Rule: R70_SOURCE_bank_specific_interface · Uses: G001
Before
source roles = [2, 3, addition_disjoint]
After
derived = [2, 3]
Conditions: none
Both branch counts are GIVEN positive integers.Addition still requires the disjointness/overlap premise,not merely two numbers.
Rule: Counting_TWO_GIVEN_branch_cardinalities · Uses: G001, S001
Before
Counting disjoint union cardinality := sum(2, 3)
After
Counting disjoint union cardinality = 5
Conditions: none
This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation.
Rule: exact_rational_arithmetic · Uses: G001, S002
Before
source roles = [2, 3]
After
derived = [5]
Conditions: none
The branches are GIVEN disjoint,so every union outcome is counted once:|A∪B|=|A|+|B|.This is not a rule without the disjointness premise.
Rule: Counting_DISJOINT_no_double_count · Uses: G001, S003
S004 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.S003 · premise_and_result_audit — Recompute Counting disjoint union cardinality with exact rational arithmetic, not rounded decimals.S002 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.S001 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.5
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: c7203d3309c0c9e23881e7218a5cce7bd3697c0470e29c3a83c75b3d02c78ec7candidate record SHA-256: 8e54e791cab4cf890a05087546ab19eb78675ea08677542d34076b35436c1d19semantic review receipt SHA-256: 9820ac6529139bd53d516c8bfdfdd41184b0cd52dad69fa433344010db37af80question-first witness SHA-256: c9c939762bbd4d3ea3403084c8e95541dc2c7e56eb82fc74eaba8c80a4517dabLean: NOT_RUN · human review: NOT_PERFORMED