ME.6.MC:4.4 - Derive the property or the separating case

Carry out the mathematical operation that can settle the question. Compose the functions, derive the resource bound, build a schedule, or explore the allowed transitions. A model name or a diagram is not yet that result.

For a preservation claim, state the condition initially and show why each allowed step retains it. For modular reasoning, establish what each contribution guarantees under its assumptions, then check that the connected contributions and environment supply those assumptions. Two contributions that each wait for the other’s result can both satisfy a conditional promise while neither starts. Progress requires an enabling basis and any needed scheduling or delivery assumptions.

For a failure claim, give the input or sequence that produces the prohibited consequence. One admitted counterexample defeats a universal assertion. Check whether it represents a possible working case; an over-broad abstraction can introduce a sequence the work cannot realize. Conversely, a model that omitted a real interaction can miss a failure. CMP.14 and the applicable mathematical interpretation supply the needed refinement.

For a finite construction, exhaustive exploration can establish the property over the explored state space. A few simulation runs establish their observed outcomes. A bound may settle the question without enumeration; if even an optimistic capacity bound misses the deadline, searching more schedules under the same conditions cannot repair that alternative.

Keep the scope of equivalence explicit. Equality of final outputs can be sufficient for a final-output question. Equality of histories, distributions or burdens requires those distinctions in the comparison. A later receiving operation may distinguish arrangements that were equivalent for the earlier use.