# Question 32065: Finite Set Membership

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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.

R0063-32065 · q-20260913-finite-set-membership-0015



## Original question and givens

Let A={141, 142, 143, 144} be an explicitly enumerated finite set. Does 144 satisfy 144∈A?


- G001 — Let A={141, 142, 143, 144} be an explicitly enumerated finite set. Does 144 satisfy 144∈A?





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





## Step-by-step derivation

S001 · impliesBefore

source roles = [qf-finite-set-membership, no-required-operation, no-required-domain, [scenario]]

After

derived = [[typed_atom_membership_YesNo_STRING]]

Conditions: none

BASE sources do not acquire a generic legacy operation/domain or unknown-metadata ban.Retain metadata WITHOUT using it as an answer oracle.PULSE/legacy enforce their exact source keys,operation/domain.Do not impose universal tuples,/1 or input bounds.

Step identifiers and dependenciesRule: R63_SOURCE_bank_keys_operation_domain_output_roles_metadata_not_oracle · Uses: G001





S002 · impliesBefore

source roles = [0, [Number, 141], [Number, 144]]

After

derived = [No]

Conditions: none

Compare EVERY ORIGINAL enumerated atom with the query by type/value.Do not identify False with0 or coerce numeric strings,and do not reject repeated enumeration.Distinct JSON reference nodes do not become the same JS object by deep equality.

Step identifiers and dependenciesRule: Membership_EACH_original_enumerated_atom_TYPE_aware_equality · Uses: G001, S001





S003 · impliesBefore

source roles = [1, [Number, 142], [Number, 144]]

After

derived = [No]

Conditions: none

Compare EVERY ORIGINAL enumerated atom with the query by type/value.Do not identify False with0 or coerce numeric strings,and do not reject repeated enumeration.Distinct JSON reference nodes do not become the same JS object by deep equality.

Step identifiers and dependenciesRule: Membership_EACH_original_enumerated_atom_TYPE_aware_equality · Uses: G001, S002





S004 · impliesBefore

source roles = [2, [Number, 143], [Number, 144]]

After

derived = [No]

Conditions: none

Compare EVERY ORIGINAL enumerated atom with the query by type/value.Do not identify False with0 or coerce numeric strings,and do not reject repeated enumeration.Distinct JSON reference nodes do not become the same JS object by deep equality.

Step identifiers and dependenciesRule: Membership_EACH_original_enumerated_atom_TYPE_aware_equality · Uses: G001, S003





S005 · impliesBefore

source roles = [3, [Number, 144], [Number, 144]]

After

derived = [Yes]

Conditions: none

Compare EVERY ORIGINAL enumerated atom with the query by type/value.Do not identify False with0 or coerce numeric strings,and do not reject repeated enumeration.Distinct JSON reference nodes do not become the same JS object by deep equality.

Step identifiers and dependenciesRule: Membership_EACH_original_enumerated_atom_TYPE_aware_equality · Uses: G001, S004





S006 · impliesBefore

source roles = [[[Number, 141], [Number, 142], [Number, 143], [Number, 144]], [Number, 144], [scenario]]

After

derived = [[No, No, No, Yes], Yes]

Conditions: none

Yes requires an ACTUAL match;No requires all comparisons false.Retain scenario/other metadata WITHOUT treating it as a truth oracle.Do not import another set bank uniqueness/SAFE/integer restriction.This frozen slice uses small integers,not universal unsafe-JS certification.

Step identifiers and dependenciesRule: Membership_COMPLETE_any_match_ignores_scenario_metadata · Uses: G001, S005









## Reverse checks


- S006 · premise_and_result_audit — Reverse-check ORIGINAL inputs,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
- S005 · premise_and_result_audit — Reverse-check ORIGINAL inputs,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
- S004 · premise_and_result_audit — Reverse-check ORIGINAL inputs,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
- S003 · premise_and_result_audit — Reverse-check ORIGINAL inputs,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
- S002 · premise_and_result_audit — Reverse-check ORIGINAL inputs,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
- S001 · premise_and_result_audit — Reverse-check ORIGINAL inputs,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.





## Result

Yes

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: 4500ef153b3b9053dfd11f1dae17ec43b613521618041f4a8034fc6b80aecf95
- candidate record SHA-256: 58a6af4231b686e23e1eb7e5a1140dce0856227e23ca86f27f3a9455a777b3b1
- semantic review receipt SHA-256: acf03b776f4855e3869810bcbecf1116e3a2b11dfb1e2a5dfbcf8135ad24a7d0
- question-first witness SHA-256: eadbbac3220988b52754f32450fb536d627217306d1ce28a49134f56c21bfa88
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20260913-finite-set-membership-0015.json)