Double dissociation

Two interventions or patient groups show opposite relative impairments on two tasks. This constrains a simple account based only on general task difficulty, but does not prove that the underlying neural circuits are independent: task sensitivity, lesion extent and alternative strategies still matter.

Suppose performances on fixed tasks $A$ and $B$ are $f_A(r)$ and $f_B(r)$, where both functions are nondecreasing in the same scalar resource $r$. If patient $P$ performs strictly better than $Q$ on $A$, then $r_P>r_Q$: the reverse ordering would contradict monotonicity. If $Q$ performs strictly better on $B$, the same argument gives $r_Q>r_P$, a contradiction. Thus a genuine crossover rejects this single-resource model.

The conclusion depends on the fixed mappings and task comparability. It does not prove isolated anatomical stores, and it need not apply when patients differ in strategy, sensory access or other task parameters.