Exercise 12.10 [part-decomposition-exercise]

Write definitions for the following:

1. ${ExhaustivePartDecomposition}$

2. ${PartPartition}$

3. ${PartwiseDisjoint}$

These should be analogous to the definitions for ${ExhaustiveDecomposition}$, ${Partition}$, and ${Disjoint}$. Is it the case that ${PartPartition}(s,{BunchOf}(s))$? If so, prove it; if not, give a counterexample and define sufficient conditions under which it does hold.