Reflecting need composition into solution decomposition

Prove that, within the $ framework for change engineering, every complex refinement of a need formed by sequential and/or parallel composition admits a corresponding reflection in the solution space that decomposes the solution into components aligned with each sub-need. Specifically, establish that when a need is refined as a composition f(N1, ..., Nn) using sequential and/or parallel operators, there exists a solution composition f(F1, ..., Fn) such that the composed solution satisfies the composed need under the formal rules of the $ micro-process.

Background

The paper introduces the $ framework, a brownfield change-engineering extension of the POE framework, with a formal micro-process based on a Gentzen-style sequent calculus. Among its rule classes are sequence and parallel change transformations, and a solution-reflection rule that mirrors need structure into solution structure.

In the extended illustrative example of a two-stage API upgrade, the authors refine the need via sequence and reflect that refinement into the solution, then note a broader expectation: that complex need refinements using sequential and parallel composition should generally be reflectable in the solution to yield component-wise alignment. They mark this expectation as a conjecture, inviting a formal proof.