# Question 33415: All Preimages of a Qualified Constant Finite Map

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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.

R0065-33415 · q-20261013-advance-20261025-r05-measurable-function-0065



## Original question and givens

Use complete qualified finite sigma-algebras in their already-canonical increasing-bit-mask order and complete total mapping tables on labels starting at 0. All set laws concern inverse images. No continuity, integrability, measure preservation or arbitrary infinite-space conclusion is inferred. source size=4, target size=4, source sigma=[[], [0], [1, 2, 3], [0, 1, 2, 3]], target sigma=[[], [0], [1], [0, 1], [2], [0, 2], [1, 2], [0, 1, 2], [3], [0, 3], [1, 3], [0, 1, 3], [2, 3], [0, 2, 3], [1, 2, 3], [0, 1, 2, 3]], constant target value=2. Give (source size,target size,value,complete constant map,every [target measurable set,preimage,source-measurable?] row,measurable?).


- G001 — Use complete qualified finite sigma-algebras in their already-canonical increasing-bit-mask order and complete total mapping tables on labels starting at 0. All set laws concern inverse images. No continuity, integrability, measure preservation or arbitrary infinite-space conclusion is inferred. source size=4, target size=4, source sigma=[[], [0], [1, 2, 3], [0, 1, 2, 3]], target sigma=[[], [0], [1], [0, 1], [2], [0, 2], [1, 2], [0, 1, 2], [3], [0, 3], [1, 3], [0, 1, 3], [2, 3], [0, 2, 3], [1, 2, 3], [0, 1, 2, 3]], constant target value=2. Give (source size,target size,value,complete constant map,every [target measurable set,preimage,source-measurable?] row,measurable?).





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





## Step-by-step derivation

S001 · impliesBefore

source roles = [qf-mod25-measdeep-constant-map-audit, measdeep-constant-map-audit, Finite_preimage_law_density, []]

After

derived = [[source_n, target_n, value, mapping, ALL_target_rows, measurable]]

Conditions: none

MOD25 uses LOCAL hyphens/named domains,legacy matrices underscores/reals;BASE logic acquires no domain/op.Output tuples,matrices,numeric fields and fraction texts follow THIS source,not a universal/1 rule.Retain originals/English/AST/status.

Step identifiers and dependenciesRule: R65_SOURCE_bank_keys_operation_domain_ordered_output_roles · Uses: G001





S002 · impliesBefore

source roles = [4, 4, [2, 2, 2, 2]]

After

derived = [[2, 2, 2, 2]]

Conditions: none

THIS source slice has carrier sizes1..7 and a typed target at EVERY original source index.Validate the WHOLE table before preimages;neither injectivity nor an inverse function is assumed.

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





S003 · impliesBefore

source roles = [ORIGINAL source sigma, 4, [[], [0], [1, 2, 3], [0, 1, 2, 3]]]

After

derived = [[0, 1, 14, 15], [[0, 1, 2, 3], [1, 2, 3], [0], []], [Yes, Yes, Yes, Yes], [[Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes]], Yes]

Conditions: none

The RAW family must ALREADY be canonical in numeric-mask order without duplicates.Check empty/full,EVERY complement and EVERY pair union;do not silently repair RAW sigma data.Complete finite closure qualifies THIS finite model,not infinite-space continuity/integrability/measure preservation.

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





S004 · impliesBefore

source roles = [TARGET sigma, 4, [[], [0], [1], [0, 1], [2], [0, 2], [1, 2], [0, 1, 2], [3], [0, 3], [1, 3], [0, 1, 3], [2, 3], [0, 2, 3], [1, 2, 3], [0, 1, 2, 3]]]

After

derived = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [[0, 1, 2, 3], [1, 2, 3], [0, 2, 3], [2, 3], [0, 1, 3], [1, 3], [0, 3], [3], [0, 1, 2], [1, 2], [0, 2], [2], [0, 1], [1], [0], []], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [[Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes]], Yes]

Conditions: none

The RAW family must ALREADY be canonical in numeric-mask order without duplicates.Check empty/full,EVERY complement and EVERY pair union;do not silently repair RAW sigma data.Complete finite closure qualifies THIS finite model,not infinite-space continuity/integrability/measure preservation.

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





S005 · impliesBefore

source roles = [CONSTANT map target event0, 0, 2, []]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

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





S006 · impliesBefore

source roles = [CONSTANT map target event0, 1, 2, []]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

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





S007 · impliesBefore

source roles = [CONSTANT map target event0, 2, 2, []]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S006





S008 · impliesBefore

source roles = [CONSTANT map target event0, 3, 2, []]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S007





S009 · impliesBefore

source roles = [CONSTANT map, 0, []]

After

derived = [[], Yes]

Conditions: none

For EVERY event in the COMPLETE target sigma,check whether its complete preimage belongs to the source sigma,not just empty/full or a sample.

Step identifiers and dependenciesRule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S008





S010 · impliesBefore

source roles = [CONSTANT map target event1, 0, 2, [0]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S009





S011 · impliesBefore

source roles = [CONSTANT map target event1, 1, 2, [0]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S010





S012 · impliesBefore

source roles = [CONSTANT map target event1, 2, 2, [0]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S011





S013 · impliesBefore

source roles = [CONSTANT map target event1, 3, 2, [0]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S012





S014 · impliesBefore

source roles = [CONSTANT map, 1, [0]]

After

derived = [[], Yes]

Conditions: none

For EVERY event in the COMPLETE target sigma,check whether its complete preimage belongs to the source sigma,not just empty/full or a sample.

Step identifiers and dependenciesRule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S013





S015 · impliesBefore

source roles = [CONSTANT map target event2, 0, 2, [1]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S014





S016 · impliesBefore

source roles = [CONSTANT map target event2, 1, 2, [1]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S015





S017 · impliesBefore

source roles = [CONSTANT map target event2, 2, 2, [1]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S016





S018 · impliesBefore

source roles = [CONSTANT map target event2, 3, 2, [1]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S017





S019 · impliesBefore

source roles = [CONSTANT map, 2, [1]]

After

derived = [[], Yes]

Conditions: none

For EVERY event in the COMPLETE target sigma,check whether its complete preimage belongs to the source sigma,not just empty/full or a sample.

Step identifiers and dependenciesRule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S018





S020 · impliesBefore

source roles = [CONSTANT map target event3, 0, 2, [0, 1]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S019





S021 · impliesBefore

source roles = [CONSTANT map target event3, 1, 2, [0, 1]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S020





S022 · impliesBefore

source roles = [CONSTANT map target event3, 2, 2, [0, 1]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S021





S023 · impliesBefore

source roles = [CONSTANT map target event3, 3, 2, [0, 1]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S022





S024 · impliesBefore

source roles = [CONSTANT map, 3, [0, 1]]

After

derived = [[], Yes]

Conditions: none

For EVERY event in the COMPLETE target sigma,check whether its complete preimage belongs to the source sigma,not just empty/full or a sample.

Step identifiers and dependenciesRule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S023





S025 · impliesBefore

source roles = [CONSTANT map target event4, 0, 2, [2]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S024





S026 · impliesBefore

source roles = [CONSTANT map target event4, 1, 2, [2]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S025





S027 · impliesBefore

source roles = [CONSTANT map target event4, 2, 2, [2]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S026





S028 · impliesBefore

source roles = [CONSTANT map target event4, 3, 2, [2]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S027





S029 · impliesBefore

source roles = [CONSTANT map, 4, [2]]

After

derived = [[0, 1, 2, 3], Yes]

Conditions: none

For EVERY event in the COMPLETE target sigma,check whether its complete preimage belongs to the source sigma,not just empty/full or a sample.

Step identifiers and dependenciesRule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S028





S030 · impliesBefore

source roles = [CONSTANT map target event5, 0, 2, [0, 2]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S029





S031 · impliesBefore

source roles = [CONSTANT map target event5, 1, 2, [0, 2]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S030





S032 · impliesBefore

source roles = [CONSTANT map target event5, 2, 2, [0, 2]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S031





S033 · impliesBefore

source roles = [CONSTANT map target event5, 3, 2, [0, 2]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S032





S034 · impliesBefore

source roles = [CONSTANT map, 5, [0, 2]]

After

derived = [[0, 1, 2, 3], Yes]

Conditions: none

For EVERY event in the COMPLETE target sigma,check whether its complete preimage belongs to the source sigma,not just empty/full or a sample.

Step identifiers and dependenciesRule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S033





S035 · impliesBefore

source roles = [CONSTANT map target event6, 0, 2, [1, 2]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S034





S036 · impliesBefore

source roles = [CONSTANT map target event6, 1, 2, [1, 2]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S035





S037 · impliesBefore

source roles = [CONSTANT map target event6, 2, 2, [1, 2]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S036





S038 · impliesBefore

source roles = [CONSTANT map target event6, 3, 2, [1, 2]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S037





S039 · impliesBefore

source roles = [CONSTANT map, 6, [1, 2]]

After

derived = [[0, 1, 2, 3], Yes]

Conditions: none

For EVERY event in the COMPLETE target sigma,check whether its complete preimage belongs to the source sigma,not just empty/full or a sample.

Step identifiers and dependenciesRule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S038





S040 · impliesBefore

source roles = [CONSTANT map target event7, 0, 2, [0, 1, 2]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S039





S041 · impliesBefore

source roles = [CONSTANT map target event7, 1, 2, [0, 1, 2]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S040





S042 · impliesBefore

source roles = [CONSTANT map target event7, 2, 2, [0, 1, 2]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S041





S043 · impliesBefore

source roles = [CONSTANT map target event7, 3, 2, [0, 1, 2]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S042





S044 · impliesBefore

source roles = [CONSTANT map, 7, [0, 1, 2]]

After

derived = [[0, 1, 2, 3], Yes]

Conditions: none

For EVERY event in the COMPLETE target sigma,check whether its complete preimage belongs to the source sigma,not just empty/full or a sample.

Step identifiers and dependenciesRule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S043





S045 · impliesBefore

source roles = [CONSTANT map target event8, 0, 2, [3]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S044





S046 · impliesBefore

source roles = [CONSTANT map target event8, 1, 2, [3]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S045





S047 · impliesBefore

source roles = [CONSTANT map target event8, 2, 2, [3]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S046





S048 · impliesBefore

source roles = [CONSTANT map target event8, 3, 2, [3]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S047





S049 · impliesBefore

source roles = [CONSTANT map, 8, [3]]

After

derived = [[], Yes]

Conditions: none

For EVERY event in the COMPLETE target sigma,check whether its complete preimage belongs to the source sigma,not just empty/full or a sample.

Step identifiers and dependenciesRule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S048





S050 · impliesBefore

source roles = [CONSTANT map target event9, 0, 2, [0, 3]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S049





S051 · impliesBefore

source roles = [CONSTANT map target event9, 1, 2, [0, 3]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S050





S052 · impliesBefore

source roles = [CONSTANT map target event9, 2, 2, [0, 3]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S051





S053 · impliesBefore

source roles = [CONSTANT map target event9, 3, 2, [0, 3]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S052





S054 · impliesBefore

source roles = [CONSTANT map, 9, [0, 3]]

After

derived = [[], Yes]

Conditions: none

For EVERY event in the COMPLETE target sigma,check whether its complete preimage belongs to the source sigma,not just empty/full or a sample.

Step identifiers and dependenciesRule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S053





S055 · impliesBefore

source roles = [CONSTANT map target event10, 0, 2, [1, 3]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S054





S056 · impliesBefore

source roles = [CONSTANT map target event10, 1, 2, [1, 3]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S055





S057 · impliesBefore

source roles = [CONSTANT map target event10, 2, 2, [1, 3]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S056





S058 · impliesBefore

source roles = [CONSTANT map target event10, 3, 2, [1, 3]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S057





S059 · impliesBefore

source roles = [CONSTANT map, 10, [1, 3]]

After

derived = [[], Yes]

Conditions: none

For EVERY event in the COMPLETE target sigma,check whether its complete preimage belongs to the source sigma,not just empty/full or a sample.

Step identifiers and dependenciesRule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S058





S060 · impliesBefore

source roles = [CONSTANT map target event11, 0, 2, [0, 1, 3]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S059





S061 · impliesBefore

source roles = [CONSTANT map target event11, 1, 2, [0, 1, 3]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S060





S062 · impliesBefore

source roles = [CONSTANT map target event11, 2, 2, [0, 1, 3]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S061





S063 · impliesBefore

source roles = [CONSTANT map target event11, 3, 2, [0, 1, 3]]

After

derived = [No]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S062





S064 · impliesBefore

source roles = [CONSTANT map, 11, [0, 1, 3]]

After

derived = [[], Yes]

Conditions: none

For EVERY event in the COMPLETE target sigma,check whether its complete preimage belongs to the source sigma,not just empty/full or a sample.

Step identifiers and dependenciesRule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S063





S065 · impliesBefore

source roles = [CONSTANT map target event12, 0, 2, [2, 3]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S064





S066 · impliesBefore

source roles = [CONSTANT map target event12, 1, 2, [2, 3]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S065





S067 · impliesBefore

source roles = [CONSTANT map target event12, 2, 2, [2, 3]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S066





S068 · impliesBefore

source roles = [CONSTANT map target event12, 3, 2, [2, 3]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S067





S069 · impliesBefore

source roles = [CONSTANT map, 12, [2, 3]]

After

derived = [[0, 1, 2, 3], Yes]

Conditions: none

For EVERY event in the COMPLETE target sigma,check whether its complete preimage belongs to the source sigma,not just empty/full or a sample.

Step identifiers and dependenciesRule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S068





S070 · impliesBefore

source roles = [CONSTANT map target event13, 0, 2, [0, 2, 3]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S069





S071 · impliesBefore

source roles = [CONSTANT map target event13, 1, 2, [0, 2, 3]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S070





S072 · impliesBefore

source roles = [CONSTANT map target event13, 2, 2, [0, 2, 3]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S071





S073 · impliesBefore

source roles = [CONSTANT map target event13, 3, 2, [0, 2, 3]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S072





S074 · impliesBefore

source roles = [CONSTANT map, 13, [0, 2, 3]]

After

derived = [[0, 1, 2, 3], Yes]

Conditions: none

For EVERY event in the COMPLETE target sigma,check whether its complete preimage belongs to the source sigma,not just empty/full or a sample.

Step identifiers and dependenciesRule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S073





S075 · impliesBefore

source roles = [CONSTANT map target event14, 0, 2, [1, 2, 3]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S074





S076 · impliesBefore

source roles = [CONSTANT map target event14, 1, 2, [1, 2, 3]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S075





S077 · impliesBefore

source roles = [CONSTANT map target event14, 2, 2, [1, 2, 3]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S076





S078 · impliesBefore

source roles = [CONSTANT map target event14, 3, 2, [1, 2, 3]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S077





S079 · impliesBefore

source roles = [CONSTANT map, 14, [1, 2, 3]]

After

derived = [[0, 1, 2, 3], Yes]

Conditions: none

For EVERY event in the COMPLETE target sigma,check whether its complete preimage belongs to the source sigma,not just empty/full or a sample.

Step identifiers and dependenciesRule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S078





S080 · impliesBefore

source roles = [CONSTANT map target event15, 0, 2, [0, 1, 2, 3]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S079





S081 · impliesBefore

source roles = [CONSTANT map target event15, 1, 2, [0, 1, 2, 3]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S080





S082 · impliesBefore

source roles = [CONSTANT map target event15, 2, 2, [0, 1, 2, 3]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S081





S083 · impliesBefore

source roles = [CONSTANT map target event15, 3, 2, [0, 1, 2, 3]]

After

derived = [Yes]

Conditions: none

Source label i lies in the PREIMAGE IFF mapping[i]belongs to the TARGET event.Keep carrier roles distinct;do not substitute a forward image.

Step identifiers and dependenciesRule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S082





S084 · impliesBefore

source roles = [CONSTANT map, 15, [0, 1, 2, 3]]

After

derived = [[0, 1, 2, 3], Yes]

Conditions: none

For EVERY event in the COMPLETE target sigma,check whether its complete preimage belongs to the source sigma,not just empty/full or a sample.

Step identifiers and dependenciesRule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S083





S085 · impliesBefore

source roles = [4, 4, 2, [2, 2, 2, 2]]

After

derived = [[[[], [], Yes], [[0], [], Yes], [[1], [], Yes], [[0, 1], [], Yes], [[2], [0, 1, 2, 3], Yes], [[0, 2], [0, 1, 2, 3], Yes], [[1, 2], [0, 1, 2, 3], Yes], [[0, 1, 2], [0, 1, 2, 3], Yes], [[3], [], Yes], [[0, 3], [], Yes], [[1, 3], [], Yes], [[0, 1, 3], [], Yes], [[2, 3], [0, 1, 2, 3], Yes], [[0, 2, 3], [0, 1, 2, 3], Yes], [[1, 2, 3], [0, 1, 2, 3], Yes], [[0, 1, 2, 3], [0, 1, 2, 3], Yes]], Yes]

Conditions: none

Every constant-map preimage is empty or the WHOLE source,both present in the QUALIFIED source sigma.Retain ALL target rows and sigma qualifications;the simple theorem does not waive RAW checks.

Step identifiers and dependenciesRule: Meas_CONSTANT_every_preimage_EMPTY_or_FULL_qualified_sigma · Uses: G001, S084









## Reverse checks


- S085 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S084 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S083 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S082 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S081 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S080 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S079 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S078 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S077 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S076 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S075 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S074 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S073 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S072 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S071 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S070 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S069 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S068 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S067 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S066 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S065 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S064 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S063 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S062 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S061 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S060 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S059 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S058 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S057 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S056 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S055 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S054 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S053 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S052 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S051 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S050 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S049 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S048 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S047 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S046 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S045 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S044 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S043 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S042 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S041 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S040 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S039 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S038 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S037 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S036 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S035 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S034 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S033 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S032 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S031 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S030 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S029 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S028 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S027 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S026 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S025 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S024 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S023 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S022 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S021 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S020 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S019 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S018 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S017 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S016 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S015 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S014 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S013 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S012 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S011 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S010 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S009 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S008 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S007 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S006 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S005 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S004 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S003 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S002 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.
- S001 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.





## Result

(4, 4, 2, [2, 2, 2, 2], [[[], [], Yes], [[0], [], Yes], [[1], [], Yes], [[0, 1], [], Yes], [[2], [0, 1, 2, 3], Yes], [[0, 2], [0, 1, 2, 3], Yes], [[1, 2], [0, 1, 2, 3], Yes], [[0, 1, 2], [0, 1, 2, 3], Yes], [[3], [], Yes], [[0, 3], [], Yes], [[1, 3], [], Yes], [[0, 1, 3], [], Yes], [[2, 3], [0, 1, 2, 3], Yes], [[0, 2, 3], [0, 1, 2, 3], Yes], [[1, 2, 3], [0, 1, 2, 3], Yes], [[0, 1, 2, 3], [0, 1, 2, 3], Yes]], 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: d8b5f3fa51f393240733c07175651cfefe7fbe0cf1e694faeca7a2cc6cbb0fca
- candidate record SHA-256: ad68854d93a01c1ed7cae703375ff80c929cd47bfe7d84da5f65f574780bcb8f
- semantic review receipt SHA-256: 92bb5fa69818f30cd2806d74a26bd5ede6c48c80d2ecc3d31a5130d4ad7666b6
- question-first witness SHA-256: 012b5aa905280d616be49aa9462daaa73bf7f6247d0a796e78bc5bcd24e6bd00
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261013-advance-20261025-r05-measurable-function-0065.json)