# Question 7295: Candidate One-Row Protocol and Total-Table Eligibility [Return to catalogue page 37](https://ocme.evemisslab.com/en/questions/page/37/) [← Question derivation index](https://ocme.evemisslab.com/en/questions/) · [Original question batch](https://ocme.evemisslab.com/en/practice/batch-20261011-advance-20261015-r03-domain-codomain-range-foundations/#q-20261011-advance-20261015-r03-domain-codomain-range-0095) This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth. R0013-07295 · q-20261011-advance-20261015-r03-domain-codomain-range-0095 ## Original question and givens Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[0, 0], [1, 1], [2, 0]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output. - G001 — Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[0, 0], [1, 1], [2, 0]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output. ## 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. - [mko-domain-codomain-range](https://ocme.evemisslab.com/en/mko/mko-domain-codomain-range/) ## Step-by-step derivation S001 · impliesBefore declared types Fin(3)→Fin(2);0-based source labels After domain,codomain and actual range remain distinct Conditions: none Fin(0) is empty;a complete total table is not a partial program function,and its actual range need not equal its declared codomain.This audits finite data,not general infinite-set theorems. Step identifiers and dependenciesRule: typed_domain_codomain_data_scope · Uses: G001 S002 · impliesBefore raw row position=0;input=0;output=0 After both ends typed=Yes Conditions: none Check both endpoint types row by row,but count every raw occurrence of a legal input even if its output is outside the codomain. Step identifiers and dependenciesRule: raw_candidate_table_row_type · Uses: G001, S001 S003 · impliesBefore raw row position=1;input=1;output=1 After both ends typed=Yes Conditions: none Check both endpoint types row by row,but count every raw occurrence of a legal input even if its output is outside the codomain. Step identifiers and dependenciesRule: raw_candidate_table_row_type · Uses: G001, S002 S004 · impliesBefore raw row position=2;input=2;output=0 After both ends typed=Yes Conditions: none Check both endpoint types row by row,but count every raw occurrence of a legal input even if its output is outside the codomain. Step identifiers and dependenciesRule: raw_candidate_table_row_type · Uses: G001, S003 S005 · impliesBefore source input=0;raw row count=1 After exactly one row=Yes Conditions: none The one-row protocol requires exactly one raw row per source.Even identical repeated values violate that format,but do not imply the deduplicated mathematical relation is multivalued. Step identifiers and dependenciesRule: one_raw_row_per_input_audit · Uses: G001, S004 S006 · impliesBefore source input=1;raw row count=1 After exactly one row=Yes Conditions: none The one-row protocol requires exactly one raw row per source.Even identical repeated values violate that format,but do not imply the deduplicated mathematical relation is multivalued. Step identifiers and dependenciesRule: one_raw_row_per_input_audit · Uses: G001, S005 S007 · impliesBefore source input=2;raw row count=1 After exactly one row=Yes Conditions: none The one-row protocol requires exactly one raw row per source.Even identical repeated values violate that format,but do not imply the deduplicated mathematical relation is multivalued. Step identifiers and dependenciesRule: one_raw_row_per_input_audit · Uses: G001, S006 S008 · impliesBefore row typing=[Yes, Yes, Yes];input counts=[1, 1, 1] After complete one-row table=Yes;ordered images=[0, 1, 0] Conditions: none Only both conditions permit orderedImages by source index.An empty source with no rows is a complete empty table;do not construct a table for an illegal candidate. Step identifiers and dependenciesRule: candidate_table_protocol_not_relation_multivaluedness · Uses: G001, S007 ## Reverse checks - S008 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S007 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S006 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - 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 ([3, 2], [Yes, Yes, Yes], [1, 1, 1], [], [], Yes, [0, 1, 0]) 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: 031258a026ce6aded2b22aef95ea162ab0aca354ed200fdf31eff9144ed1b4c7 - candidate record SHA-256: 608423d168acd51bd2e3e658e6d2302a71de6ae086b2d1635571947b47725ba7 - semantic review receipt SHA-256: e89fc6d4a50a4a7fc942c6c8939a92f835e30105a9a5850e37dd198f31c1ed59 - question-first witness SHA-256: 0e1039f4cf022bf35af4e5531651c9a2b7ca7a5fdacac34fb1e4bcd9a81f6299 - Lean: NOT_RUN · human review: NOT_PERFORMED [Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261011-advance-20261015-r03-domain-codomain-range-0095.json)