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R0009-05151 · q-20261008-advance-20261011-r05-subset-0001
Finite integer sets A=[] and B=[1]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.
G001 — Finite integer sets A=[] and B=[1]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.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
A=[];B=[1];same integer type
After
A⊆B means every A-element belongs to B
Conditions: none
An inclusion obstruction must belong to A but not B;an element outside A is no witness,and empty A gives no obstruction.
Rule: set_inclusion_definition · Uses: G001
Before
[]
After
A⊆B=Yes
Conditions: none
Because every A-element was checked,the empty obstruction set is equivalent to this finite inclusion.
Rule: complete_inclusion_obstruction_inventory · Uses: G001, S001
S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.[]
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: 1dd63ec7c3aa1769f74025d6952e89c34f75a9738980cdc091a92b9efe2abfe7candidate record SHA-256: 9c93c34274a8277782e1d66f03fcde0f0e492405873ca7f49d5569843c5e1ed8semantic review receipt SHA-256: 71e7db519df31f3a164533e472e293cb64f001b475a8d002b4a5c2740a237b56question-first witness SHA-256: 5a43f4f81b6256281f8d139a4010bbde127be803c528e5878857269c8f854462Lean: NOT_RUN · human review: NOT_PERFORMED