Samplinglib
Lean gate not recorded for this source state main · 0e31a3cda412

AutoSamplingTheory.SALD.gronwallContract

Data definition / provenance and workflow record

Meaning and type

The result has data type AutoSamplingTheory.TheoremContract. 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 gronwallContract : TheoremContract

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)

Contract identifier.

ASTIS.SALD.gronwall
title : String (explicit)

Human-readable intended theorem/lemma title.

Gronwall inequality used by SALD KL bounds
mode : String (explicit)

Workflow mode as String, not a theorem assumption.

faithfulPaper
source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor for the intended claim.

AutoSamplingTheory.SALD.saldGronwallSource — audited data reference, not expanded and not a compiled dependency edge
targetLean : String (explicit)

Target Lean file/name as recorded text, not a declaration reference with type checking.

AutoSamplingTheory/SALD.lean
statementSummary : String (explicit)

Prose summary of intended content; no Prop is proved by this field.

Differential inequality dK/dt <= -a_t K_t + b_t implies the integrated exponential bound.
proofStatus : AutoSamplingTheory.ProofStatus (explicit)

Stored ProofStatus; defaults to contractOnly.

AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
obligations : List AutoSamplingTheory.ProofObligation (explicit)

List of ProofObligation data attached to the contract; defaults to empty, which does not certify completeness.

Ordered data items

  1. AutoSamplingTheory.SALD.gronwallAnalyticObligation — audited data reference, not expanded and not a compiled dependency edge
  2. AutoSamplingTheory.SALD.gronwallEndpointCalculusObligation — audited data reference, not expanded and not a compiled dependency edge
  3. AutoSamplingTheory.SALD.gronwallExponentRewriteObligation — audited data reference, not expanded and not a compiled dependency edge
  4. AutoSamplingTheory.SALD.cycle36GronwallUpperObligation — audited data reference, not expanded and not a compiled dependency edge
  5. AutoSamplingTheory.SALD.cycle36GronwallMiddleObligation — audited data reference, not expanded and not a compiled dependency edge
  6. AutoSamplingTheory.SALD.cycle41GronwallMiddleObligation — audited data reference, not expanded and not a compiled dependency edge
  7. AutoSamplingTheory.SALD.cycle41GronwallLowerObligation — audited data reference, not expanded and not a compiled dependency edge
  8. AutoSamplingTheory.SALD.firstAppendixMiddleAuditObligation — audited data reference, not expanded and not a compiled dependency edge
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 gronwallContract : TheoremContract where
  id := "ASTIS.SALD.gronwall"
  title := "Gronwall inequality used by SALD KL bounds"
  mode := "faithfulPaper"
  source := saldGronwallSource
  targetLean := "AutoSamplingTheory/SALD.lean"
  statementSummary := "Differential inequality dK/dt <= -a_t K_t + b_t implies the integrated exponential bound."
  proofStatus := ProofStatus.obligation
  obligations := [
    gronwallAnalyticObligation,
    gronwallEndpointCalculusObligation,
    gronwallExponentRewriteObligation,
    cycle36GronwallUpperObligation,
    cycle36GronwallMiddleObligation,
    cycle41GronwallMiddleObligation,
    cycle41GronwallLowerObligation,
    firstAppendixMiddleAuditObligation
  ]

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