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Question 5001: Partition of an Explicit Candidate Set

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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R0009-05001 · q-20261008-advance-20261011-r04-set-0051

Original question and givens

Finite integer set A=[]; raw candidates=[] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.

  • G001 — Finite integer set A=[]; raw candidates=[] are treated as a set. Give (candidates belonging to A, candidates outside A), each sorted increasingly.

Definition and scope

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.

Step-by-step derivation

S001 · implies

Before

raw integer list=[]

After

extensional set=[]

Conditions: none

A set depends on its elements;deduplication and numeric ordering do not change membership.The original list is retained as source.

Step identifiers and dependencies

Rule: set_extensionality_normalization · Uses: G001

S002 · implies

Before

[]

After

([], [])

Conditions: none

The two parts are disjoint and cover the deduplicated candidate set;list members of A before nonmembers.

Step identifiers and dependencies

Rule: candidate_set_partition_complete · Uses: G001, S001

Reverse checks

  • 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.

Result

([], [])

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

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.

Source hashes and review receipts
  • input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
  • original question SHA-256: ae9f59d4887858a0304d91c879387dbc75526f2e006913bc32afcf2fd4fbb7c6
  • candidate record SHA-256: cba79904868e58b9b9a50eba6629faefa72a3adaf5747c9f2a76fd16d228df52
  • semantic review receipt SHA-256: 71e7db519df31f3a164533e472e293cb64f001b475a8d002b4a5c2740a237b56
  • question-first witness SHA-256: 5a43f4f81b6256281f8d139a4010bbde127be803c528e5878857269c8f854462
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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