Reverse insertion endpoints for the evaluated-slice paper chain #
This module re-exports the two reverse eq:add-an-a bounds used after the
paper line-87 phase-five removal and packages them into the combined phase-67
bridge consumed by ProcessedG.lean.
theorem
MIPStarRE.LDT.Commutativity.evaluatedSlice_phaseSixSeven_reverse_bound
{ι : Type u_1}
[Fintype ι]
[DecidableEq ι]
(params : Parameters)
[FieldModel params.q]
(strategy : SymStrat params.next ι)
(zeta : Error)
(hnorm : strategy.state.IsNormalized)
(family : IdxPolyFamily params ι)
(hcombined_fst :
SDDRel strategy.state (uniformDistribution (EvaluatedSliceQuestion params))
(fun (q : EvaluatedSliceQuestion params) => evaluatedPointFamilyLeft params family q.1)
(fun (q : EvaluatedSliceQuestion params) =>
Preliminaries.totalSandwichFamily (evaluatedPointFamily params family) (evaluatedSlicePointMeas params strategy)
q.1)
(4 * zeta))
(hcombined_snd :
SDDRel strategy.state (uniformDistribution (EvaluatedSliceQuestion params))
(fun (q : EvaluatedSliceQuestion params) => evaluatedPointFamilyLeft params family q.2)
(fun (q : EvaluatedSliceQuestion params) =>
Preliminaries.totalSandwichFamily (evaluatedPointFamily params family) (evaluatedSlicePointMeas params strategy)
q.2)
(4 * zeta))
:
have 𝒟 := uniformDistribution (EvaluatedSliceQuestion params);
have phase5PaperRemoved := evaluatedSlicePhaseFivePaperRemoved params strategy family;
have phase7GonnaCite := evaluatedSlicePhaseSevenGonnaCite params strategy family;
|avgOver 𝒟 phase5PaperRemoved - avgOver 𝒟 phase7GonnaCite| ≤ 4 * √zeta
Paper lines 99--104: the combined phase-67 reverse-insertion bridge.
The scalar-chain assembly only needs the endpoint comparison from the paper
line-87/eq:gcom10 term to eq:gonna-cite-this-in-just-a-bit. This lemma
packages the two proved eq:add-an-a reverse insertions (2√ζ each) through
one triangle inequality, so downstream code no longer has to carry the
intermediate phase-six endpoint.