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theorem proved term proof high

firstPassProgram_pipelines_nodup

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The list of first-pass pipeline specifications contains no duplicate entries. Researchers assembling the Option A empirical program certificate cite this to confirm metadata collision-freeness for the pipeline component. The proof is a direct term reduction to the no-duplicates result on the mapped schedule.

claimThe sequence of pipeline specifications obtained by mapping the specification function over the first-pass schedule contains no repeated entries.

background

The Option A empirical program module assembles a single certificate for the first-pass program, confirming completeness and collision-freeness at the metadata layer after separate proofs for queue, schedule, actions, deliverables, pipelines, and readiness. First-pass pipelines are the list of pipeline records produced in schedule order. The upstream no-duplicates theorem for these pipelines follows from unfolding the map definition and applying the injectivity of the pipeline specification map to the already-proven no-duplicates property of the schedule.

proof idea

The proof is a one-line term wrapper that applies the no-duplicates theorem for first-pass pipelines.

why it matters in Recognition Science

This result supplies the pipelines no-duplicates condition required by the empirical program certificate. It closes one piece of the metadata collision-free property for the assembled first-pass program. The certificate definition collects length, readiness, completeness, and injectivity facts to certify the Option A program as ready without internal conflicts.

scope and limits

formal statement (Lean)

  89theorem firstPassProgram_pipelines_nodup :
  90    firstPassPipelines.Nodup :=

proof body

Term-mode proof.

  91  firstPassPipelines_nodup
  92
  93/-- First-pass completion gate: every scheduled row is ready and every output

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