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Question 33416: All Preimages of a Qualified Constant Finite Map

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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R0065-33416 · q-20261013-advance-20261025-r05-measurable-function-0066

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=[[], [1], [0, 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=3. 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=[[], [1], [0, 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=3. 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.

Step-by-step derivation

S001 · implies

Before

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 dependencies

Rule: R65_SOURCE_bank_keys_operation_domain_ordered_output_roles · Uses: G001

S002 · implies

Before

source roles = [4, 4, [3, 3, 3, 3]]

After

derived = [[3, 3, 3, 3]]

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 dependencies

Rule: Meas_RAW_complete_total_map_typed_NONEMPTY_carriers · Uses: G001, S001

S003 · implies

Before

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

After

derived = [[0, 2, 13, 15], [[0, 1, 2, 3], [0, 2, 3], [1], []], [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 dependencies

Rule: Meas_SIGMA_ALREADY_canonical_MASK_order_EMPTY_FULL_ALL_closures · Uses: G001, S002

S004 · implies

Before

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 dependencies

Rule: Meas_SIGMA_ALREADY_canonical_MASK_order_EMPTY_FULL_ALL_closures · Uses: G001, S003

S005 · implies

Before

source roles = [CONSTANT map target event0, 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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S004

S006 · implies

Before

source roles = [CONSTANT map target event0, 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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S005

S007 · implies

Before

source roles = [CONSTANT map target event0, 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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S006

S008 · implies

Before

source roles = [CONSTANT map target event0, 3, 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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S007

S009 · implies

Before

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 dependencies

Rule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S008

S010 · implies

Before

source roles = [CONSTANT map target event1, 0, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S009

S011 · implies

Before

source roles = [CONSTANT map target event1, 1, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S010

S012 · implies

Before

source roles = [CONSTANT map target event1, 2, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S011

S013 · implies

Before

source roles = [CONSTANT map target event1, 3, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S012

S014 · implies

Before

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 dependencies

Rule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S013

S015 · implies

Before

source roles = [CONSTANT map target event2, 0, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S014

S016 · implies

Before

source roles = [CONSTANT map target event2, 1, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S015

S017 · implies

Before

source roles = [CONSTANT map target event2, 2, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S016

S018 · implies

Before

source roles = [CONSTANT map target event2, 3, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S017

S019 · implies

Before

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 dependencies

Rule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S018

S020 · implies

Before

source roles = [CONSTANT map target event3, 0, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S019

S021 · implies

Before

source roles = [CONSTANT map target event3, 1, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S020

S022 · implies

Before

source roles = [CONSTANT map target event3, 2, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S021

S023 · implies

Before

source roles = [CONSTANT map target event3, 3, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S022

S024 · implies

Before

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 dependencies

Rule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S023

S025 · implies

Before

source roles = [CONSTANT map target event4, 0, 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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S024

S026 · implies

Before

source roles = [CONSTANT map target event4, 1, 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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S025

S027 · implies

Before

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

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S026

S028 · implies

Before

source roles = [CONSTANT map target event4, 3, 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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S027

S029 · implies

Before

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

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 dependencies

Rule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S028

S030 · implies

Before

source roles = [CONSTANT map target event5, 0, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S029

S031 · implies

Before

source roles = [CONSTANT map target event5, 1, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S030

S032 · implies

Before

source roles = [CONSTANT map target event5, 2, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S031

S033 · implies

Before

source roles = [CONSTANT map target event5, 3, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S032

S034 · implies

Before

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

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 dependencies

Rule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S033

S035 · implies

Before

source roles = [CONSTANT map target event6, 0, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S034

S036 · implies

Before

source roles = [CONSTANT map target event6, 1, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S035

S037 · implies

Before

source roles = [CONSTANT map target event6, 2, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S036

S038 · implies

Before

source roles = [CONSTANT map target event6, 3, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S037

S039 · implies

Before

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

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 dependencies

Rule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S038

S040 · implies

Before

source roles = [CONSTANT map target event7, 0, 3, [0, 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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S039

S041 · implies

Before

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

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S040

S042 · implies

Before

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

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S041

S043 · implies

Before

source roles = [CONSTANT map target event7, 3, 3, [0, 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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S042

S044 · implies

Before

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

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 dependencies

Rule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S043

S045 · implies

Before

source roles = [CONSTANT map target event8, 0, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S044

S046 · implies

Before

source roles = [CONSTANT map target event8, 1, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S045

S047 · implies

Before

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

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S046

S048 · implies

Before

source roles = [CONSTANT map target event8, 3, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S047

S049 · implies

Before

source roles = [CONSTANT map, 8, [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 dependencies

Rule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S048

S050 · implies

Before

source roles = [CONSTANT map target event9, 0, 3, [0, 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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S049

S051 · implies

Before

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

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S050

S052 · implies

Before

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

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S051

S053 · implies

Before

source roles = [CONSTANT map target event9, 3, 3, [0, 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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S052

S054 · implies

Before

source roles = [CONSTANT map, 9, [0, 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 dependencies

Rule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S053

S055 · implies

Before

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

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S054

S056 · implies

Before

source roles = [CONSTANT map target event10, 1, 3, [1, 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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S055

S057 · implies

Before

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

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S056

S058 · implies

Before

source roles = [CONSTANT map target event10, 3, 3, [1, 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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S057

S059 · implies

Before

source roles = [CONSTANT map, 10, [1, 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 dependencies

Rule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S058

S060 · implies

Before

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

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S059

S061 · implies

Before

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

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S060

S062 · implies

Before

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

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S061

S063 · implies

Before

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

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S062

S064 · implies

Before

source roles = [CONSTANT map, 11, [0, 1, 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 dependencies

Rule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S063

S065 · implies

Before

source roles = [CONSTANT map target event12, 0, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S064

S066 · implies

Before

source roles = [CONSTANT map target event12, 1, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S065

S067 · implies

Before

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

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S066

S068 · implies

Before

source roles = [CONSTANT map target event12, 3, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S067

S069 · implies

Before

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 dependencies

Rule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S068

S070 · implies

Before

source roles = [CONSTANT map target event13, 0, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S069

S071 · implies

Before

source roles = [CONSTANT map target event13, 1, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S070

S072 · implies

Before

source roles = [CONSTANT map target event13, 2, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S071

S073 · implies

Before

source roles = [CONSTANT map target event13, 3, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S072

S074 · implies

Before

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 dependencies

Rule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S073

S075 · implies

Before

source roles = [CONSTANT map target event14, 0, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S074

S076 · implies

Before

source roles = [CONSTANT map target event14, 1, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S075

S077 · implies

Before

source roles = [CONSTANT map target event14, 2, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S076

S078 · implies

Before

source roles = [CONSTANT map target event14, 3, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S077

S079 · implies

Before

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 dependencies

Rule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S078

S080 · implies

Before

source roles = [CONSTANT map target event15, 0, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S079

S081 · implies

Before

source roles = [CONSTANT map target event15, 1, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S080

S082 · implies

Before

source roles = [CONSTANT map target event15, 2, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S081

S083 · implies

Before

source roles = [CONSTANT map target event15, 3, 3, [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 dependencies

Rule: Meas_PREIMAGE_EACH_source_label_target_membership · Uses: G001, S082

S084 · implies

Before

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 dependencies

Rule: Meas_EVERY_target_sigma_event_complete_preimage_source_membership · Uses: G001, S083

S085 · implies

Before

source roles = [4, 4, 3, [3, 3, 3, 3]]

After

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

Rule: 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, 3, [3, 3, 3, 3], [[[], [], Yes], [[0], [], Yes], [[1], [], Yes], [[0, 1], [], Yes], [[2], [], Yes], [[0, 2], [], Yes], [[1, 2], [], Yes], [[0, 1, 2], [], Yes], [[3], [0, 1, 2, 3], Yes], [[0, 3], [0, 1, 2, 3], Yes], [[1, 3], [0, 1, 2, 3], Yes], [[0, 1, 3], [0, 1, 2, 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: ed9a3a59d80ca58296a0c60ec290f2fe43c4673f243df6f37679d48d95a44f0a
  • candidate record SHA-256: 9ebb5491381a1bd32f51f7026ad30fbe85b20265b233b4b41f0bf4abdadf9c3f
  • semantic review receipt SHA-256: 92bb5fa69818f30cd2806d74a26bd5ede6c48c80d2ecc3d31a5130d4ad7666b6
  • question-first witness SHA-256: 012b5aa905280d616be49aa9462daaa73bf7f6247d0a796e78bc5bcd24e6bd00
  • Lean: NOT_RUN · human review: NOT_PERFORMED
Same-source full JSON