# Question 8307: Typed Relation Projections and Missing Sources

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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.

R0015-08307 · q-20261012-advance-20261017-r03-relation-0007



## Original question and givens

The explicitly typed relation R⊆Fin(3)×Fin(3) has ordered pairs=[[0, 1]]. Normalize repeated pairs as a set, in lexicographic order. A relation need not be single-valued or total; its converse need not be an inverse function. Give ([n,m], normalized pairs, source projection, target projection, pair count, missing source labels).


- G001 — The explicitly typed relation R⊆Fin(3)×Fin(3) has ordered pairs=[[0, 1]]. Normalize repeated pairs as a set, in lexicographic order. A relation need not be single-valued or total; its converse need not be an inverse function. Give ([n,m], normalized pairs, source projection, target projection, pair count, missing source labels).





## 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-relation](https://ocme.evemisslab.com/en/mko/mko-relation/)





## Step-by-step derivation

S001 · impliesBefore

types=(3,3);raw ordered pairs=[[0, 1]]

After

normalized relation=[[0, 1]]

Conditions: none

Validate both types of every ordered pair,then deduplicate identical pairs.Swapping coordinates forms the converse,not a sorting of one pair.A relation may be multivalued or partial.

Step identifiers and dependenciesRule: typed_relation_set_normalization · Uses: G001





S002 · impliesBefore

normalized pairs=[[0, 1]];declared sources=[0, 1, 2]

After

source projection=[0];target projection=[1];missing sources=[1, 2];count=1

Conditions: none

Collect and deduplicate first and second coordinates separately.Declared source labels need not occur in the relation;do not invent values for them.

Step identifiers and dependenciesRule: relation_coordinate_projections · 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

([3, 3], [[0, 1]], [0], [1], 1, [1, 2])

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: 079dcc6db17c9c02d2ed24f17673be885e9acb46c9f0a2696917979d6d4d54da
- candidate record SHA-256: 3665d1f24aac1bab41352ca4a8d62bc681b602afec316f3fe1955df974b0c875
- semantic review receipt SHA-256: 6ecad9d909199221a07e923f87425e80b3bdec3eed46fe5910d04fca694cae18
- question-first witness SHA-256: e8f00458977a09493b5f9f05ab9e6feec72debaf4c7d1c609d1fc95900a35a1b
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261012-advance-20261017-r03-relation-0007.json)