AutoSamplingTheory.SALD.cycle41GronwallLowerObligation

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 cycle41GronwallLowerObligation : 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.cycle41_interior_endpoint_bridge

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 41 lower proof-producing endpoint-safe Gronwall bridge for appendix.tex lines 62-69: SALD.gronwallOrderIntegrationOfHasDerivRight uses Mathlib's right-derivative FTC with continuity on [0,t1] and derivatives only on (0,t1); SALD.gronwallIntegratingFactorBoundOfInteriorDerivatives assembles the displayed Gronwall bound with no endpoint derivative hypotheses on the integrating-factor product; SALD.gronwallIntegratingFactorBoundOfInteriorContinuousData and SALD.gronwallIntegratingFactorBoundOfInteriorC1 discharge the continuity/integrability side conditions under a C1-compatible source interpretation.

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.cycle41GronwallMiddleObligation
2. SALD.gronwallOrderIntegrationOfHasDerivRight
3. SALD.gronwallIntegratingFactorBoundOfInteriorDerivatives
4. SALD.gronwallIntegratingFactorBoundOfInteriorContinuousData
5. SALD.gronwallIntegratingFactorBoundOfInteriorC1
6. SALD.gronwallEndpointEvaluationScalar
7. SALD.gronwallEndpointMultiplyByExpNegScalar
8. SALD.gronwallEndpointIntegralRewrite
9. sald.gronwall.endpoint_calculus
10. sald.gronwall.integrating_factor

note : String (explicit)

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

This closes one endpoint-safe calculus layer by eliminating endpoint derivative hypotheses from the FTC/order-integration assembly. SALD.gronwallContract remains ProofStatus.obligation because the paper's phrase differentiable on [0,t1] still has to be identified with this C1-compatible or absolute-continuity backend before the source lemma can be marked formalized.

def cycle41GronwallLowerObligation : ProofObligation where
  id := "sald.gronwall.cycle41_interior_endpoint_bridge"
  statement := "Record the cycle 41 lower proof-producing endpoint-safe Gronwall bridge for appendix.tex lines 62-69: SALD.gronwallOrderIntegrationOfHasDerivRight uses Mathlib's right-derivative FTC with continuity on [0,t1] and derivatives only on (0,t1); SALD.gronwallIntegratingFactorBoundOfInteriorDerivatives assembles the displayed Gronwall bound with no endpoint derivative hypotheses on the integrating-factor product; SALD.gronwallIntegratingFactorBoundOfInteriorContinuousData and SALD.gronwallIntegratingFactorBoundOfInteriorC1 discharge the continuity/integrability side conditions under a C1-compatible source interpretation."
  source := saldGronwallSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle41GronwallMiddleObligation",
    "SALD.gronwallOrderIntegrationOfHasDerivRight",
    "SALD.gronwallIntegratingFactorBoundOfInteriorDerivatives",
    "SALD.gronwallIntegratingFactorBoundOfInteriorContinuousData",
    "SALD.gronwallIntegratingFactorBoundOfInteriorC1",
    "SALD.gronwallEndpointEvaluationScalar",
    "SALD.gronwallEndpointMultiplyByExpNegScalar",
    "SALD.gronwallEndpointIntegralRewrite",
    "sald.gronwall.endpoint_calculus",
    "sald.gronwall.integrating_factor"
  ]
  note := "This closes one endpoint-safe calculus layer by eliminating endpoint derivative hypotheses from the FTC/order-integration assembly. SALD.gronwallContract remains ProofStatus.obligation because the paper's phrase differentiable on [0,t1] still has to be identified with this C1-compatible or absolute-continuity backend before the source lemma can be marked formalized."