AutoSamplingTheory.SALD.cycle36GronwallMiddleObligation

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 cycle36GronwallMiddleObligation : 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.gronwall.cycle36_middle_assembly

statement : String (explicit)

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

Record the cycle 36 proof-producing assembly for appendix.tex lines 58-69: SALD.gronwallEndpointIntegralRewrite moves the endpoint inverse integrating factor through the b_t integral, SALD.gronwallIntegratingFactorBoundOfDerivatives assembles the full displayed Gronwall bound from explicit global derivative/integrability hypotheses, SALD.gronwallIntegratingFactorBoundOfIntegral discharges the derivative of int_0^t a using Mathlib's interval-integral FTC at each point, and SALD.gronwallIntegratingFactorBoundOfContinuousData proves the displayed bound from global continuity of a, b, K, and K' plus the derivative inequality.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGronwallSource — 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.cycle36GronwallUpperPacket
2. SALD.gronwallEndpointIntegralRewrite
3. SALD.gronwallIntegratingFactorBoundOfDerivatives
4. SALD.gronwallIntegratingFactorBoundOfIntegral
5. SALD.gronwallIntegratingFactorProductDerivative
6. SALD.gronwallIntegratingFactorDerivativeInequalityScalar
7. SALD.gronwallOrderIntegrationOfHasDerivAt
8. SALD.gronwallEndpointEvaluationScalar
9. SALD.gronwallEndpointMultiplyByExpNegScalar
10. SALD.gronwallExpProductRewriteIntegralCongr
11. SALD.gronwallCoefficientSideConditionsOfContinuous
12. SALD.gronwallIntegratingFactorBoundOfContinuousData
13. sald.gronwall.endpoint_calculus
14. sald.gronwall.exponent_rewrite

note : String (explicit)

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

The Lean theorems are formalized local Gronwall assembly under explicit Mathlib side conditions. The lower continuous-data wrapper removes the separate integrability and coefficient-FTC assumptions when a, b, K, and K' are globally continuous, but it still does not prove that the paper's concise differentiability-on-[0,t1] hypothesis supplies a globally continuous derivative witness or the endpoint-safe derivative semantics. SALD.gronwallContract remains ProofStatus.obligation.

def cycle36GronwallMiddleObligation : ProofObligation where
  id := "sald.gronwall.cycle36_middle_assembly"
  statement := "Record the cycle 36 proof-producing assembly for appendix.tex lines 58-69: SALD.gronwallEndpointIntegralRewrite moves the endpoint inverse integrating factor through the b_t integral, SALD.gronwallIntegratingFactorBoundOfDerivatives assembles the full displayed Gronwall bound from explicit global derivative/integrability hypotheses, SALD.gronwallIntegratingFactorBoundOfIntegral discharges the derivative of int_0^t a using Mathlib's interval-integral FTC at each point, and SALD.gronwallIntegratingFactorBoundOfContinuousData proves the displayed bound from global continuity of a, b, K, and K' plus the derivative inequality."
  source := saldGronwallSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle36GronwallUpperPacket",
    "SALD.gronwallEndpointIntegralRewrite",
    "SALD.gronwallIntegratingFactorBoundOfDerivatives",
    "SALD.gronwallIntegratingFactorBoundOfIntegral",
    "SALD.gronwallIntegratingFactorProductDerivative",
    "SALD.gronwallIntegratingFactorDerivativeInequalityScalar",
    "SALD.gronwallOrderIntegrationOfHasDerivAt",
    "SALD.gronwallEndpointEvaluationScalar",
    "SALD.gronwallEndpointMultiplyByExpNegScalar",
    "SALD.gronwallExpProductRewriteIntegralCongr",
    "SALD.gronwallCoefficientSideConditionsOfContinuous",
    "SALD.gronwallIntegratingFactorBoundOfContinuousData",
    "sald.gronwall.endpoint_calculus",
    "sald.gronwall.exponent_rewrite"
  ]
  note := "The Lean theorems are formalized local Gronwall assembly under explicit Mathlib side conditions. The lower continuous-data wrapper removes the separate integrability and coefficient-FTC assumptions when a, b, K, and K' are globally continuous, but it still does not prove that the paper's concise differentiability-on-[0,t1] hypothesis supplies a globally continuous derivative witness or the endpoint-safe derivative semantics. SALD.gronwallContract remains ProofStatus.obligation."

/-- Cycle-41 middle proof-producing Gronwall derivative-source wrapper. -/