AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteCondDistribIntegralMathlibSource

Data definition / provenance and workflow record

Meaning and type

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

Lean statement of this data definition

The part after the colon is the output data type. This declaration takes no mathematical proof inputs.

def saldGeneralMovingTargetDiscreteCondDistribIntegralMathlibSource :
    SourceAnchor

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.

key : String (explicit): Stable source/group identifier; multiple anchors may share it.
mathlib-condDistrib-compProd-integral
kind : AutoSamplingTheory.SourceKind (explicit): SourceKind taxonomy tag identifying paper/localTex/externalLean/mathlib/citedResult/experimentNote.
AutoSamplingTheory.SourceKind.mathlib — stored label only; no proof certification
pathOrUrl : String (explicit): Recorded location string; may be a local source path, package path, or URL. Existence and revision are not certified by the field.
.lake/packages/mathlib/Mathlib/Probability/Kernel/CondDistrib.lean
label : String (explicit): Recorded equation/theorem/proof label or declaration/search target. It may be composite or descriptive, not necessarily a resolvable Lean declaration.
ProbabilityTheory.compProd_map_condDistrib; MeasureTheory.Measure.integral_compProd
note : String (explicit): Human-authored scope, line-range, reuse, or caveat text. It is stored prose, not a checked assertion.
Mathlib disintegration and composition-product integral identities used to turn the canonical condDistrib component integral for X_k^eta | hat X_s into a sample-law weak pairing in appendix.tex lines 1368-1377.

Exact Lean data construction

Each field assignment stores the corresponding value shown above. Omitted fields use the explicitly identified schema defaults. Strings that name theorems remain strings; they do not call those theorems.

def saldGeneralMovingTargetDiscreteCondDistribIntegralMathlibSource :
    SourceAnchor where
  key := "mathlib-condDistrib-compProd-integral"
  kind := SourceKind.mathlib
  pathOrUrl := ".lake/packages/mathlib/Mathlib/Probability/Kernel/CondDistrib.lean"
  label := "ProbabilityTheory.compProd_map_condDistrib; MeasureTheory.Measure.integral_compProd"
  note := "Mathlib disintegration and composition-product integral identities used to turn the canonical condDistrib component integral for X_k^eta | hat X_s into a sample-law weak pairing in appendix.tex lines 1368-1377."

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