AutoSamplingTheory.SALD.cycle115GeneralMovingTargetDiscreteNamedBarBCondExpSourceLowerObligation

Data definition / provenance and workflow record

Meaning and type

The result has data type AutoSamplingTheory.ProofObligation. A value of this type stores descriptions; it is not a proof of the statements in those descriptions.

def cycle115GeneralMovingTargetDiscreteNamedBarBCondExpSourceLowerObligation :
    ProofObligation

Construction and field-by-field explanation

Construct a data record from explicit fields and the audited defaults shown below.

This Lean definition constructs provenance or workflow data. It does not prove the mathematical statements stored as text. Status labels, named dependencies and citations are data, not compilation, proof or source certificates.

id : String (explicit)

Stable obligation identifier.

sald.general_moving_target_discrete.cycle115_named_barB_condExp_source_lower

statement : String (explicit)

Desired mathematical or workflow content as String; it is not a proposition in Prop and the def does not prove it.

Cycle 115 lower compiles SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCondExpSourceDef for appendix.tex:1368-1377. Classification: discharges-supplied-hypothesis. The exact supplied hypothesis discharged is hbarBAe in SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalAeEq: the theorem derives the selected-to-canonical hatRhoS-a.e. equality from SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpSourceDef and the paper's sample-space conditional-expectation representative hbarBCondExp, then reuses the cycle-115 middle theorem to obtain Integrable barB hatRhoS and hbarBStateSetIntegral. Remaining exact boundary: prove hbarBCondExp for the paper-selected conditional-expectation representative, with hbarBEqMeas supplied by the existing cycle-110 measurable-representative route if not source-supplied.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteConditionalDriftSource — audited data reference, not expanded and not a compiled dependency edge

status : AutoSamplingTheory.ProofStatus (explicit)

Stored ProofStatus, default obligation; even an explicitly stored formalized does not independently certify a Lean theorem.

AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification

dependsOn : List String (explicit)

List of declared dependency names as strings; may mix theorem names, obligations, source labels, or descriptions. Not the compiled dependency DAG.

Ordered data items

1. SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCondExpSourceDef
2. SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpSourceDef
3. SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalAeEq
4. SALD.generalMovingTargetDiscreteCondDistribNamedBarBEqMeasOfStronglyMeasurable
5. ASTIS.SALD.cycle115.remaining_named_barB_selected_canonical_ae_eq
6. ASTIS.SALD.cycle110.remaining_condExp_source_representative_after_eq_meas
7. appendix.tex:1368-1377
8. sald.general_moving_target_discrete.em_interpolation_fp

note : String (explicit)

Recorded evidence/caveats; may distinguish a compiled scalar helper from still-open source analysis.

Dynamic-leaf lower theorem only. It removes the supplied hbarBAe equality from the selected-version bridge using the already source-cited conditional-expectation definition route. It does not prove weak FP, KL derivative, LSI, DV, Gronwall, theorem-status promotion, SLT import, Lake change, source-index rebaseline, or sald_version_2 content.

def cycle115GeneralMovingTargetDiscreteNamedBarBCondExpSourceLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle115_named_barB_condExp_source_lower"
  statement := "Cycle 115 lower compiles SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCondExpSourceDef for appendix.tex:1368-1377. Classification: discharges-supplied-hypothesis. The exact supplied hypothesis discharged is hbarBAe in SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalAeEq: the theorem derives the selected-to-canonical hatRhoS-a.e. equality from SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpSourceDef and the paper's sample-space conditional-expectation representative hbarBCondExp, then reuses the cycle-115 middle theorem to obtain Integrable barB hatRhoS and hbarBStateSetIntegral. Remaining exact boundary: prove hbarBCondExp for the paper-selected conditional-expectation representative, with hbarBEqMeas supplied by the existing cycle-110 measurable-representative route if not source-supplied."
  source := saldGeneralMovingTargetDiscreteConditionalDriftSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCondExpSourceDef",
    "SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpSourceDef",
    "SALD.generalMovingTargetDiscreteNamedBarBStateEventIntegralAndIntegrableOfCanonicalAeEq",
    "SALD.generalMovingTargetDiscreteCondDistribNamedBarBEqMeasOfStronglyMeasurable",
    "ASTIS.SALD.cycle115.remaining_named_barB_selected_canonical_ae_eq",
    "ASTIS.SALD.cycle110.remaining_condExp_source_representative_after_eq_meas",
    "appendix.tex:1368-1377",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf lower theorem only. It removes the supplied hbarBAe equality from the selected-version bridge using the already source-cited conditional-expectation definition route. It does not prove weak FP, KL derivative, LSI, DV, Gronwall, theorem-status promotion, SLT import, Lake change, source-index rebaseline, or sald_version_2 content."

/-- Cycle-115 proof-DAG pane for the selected named `barB` version boundary. -/