renamed emptyparts1 → emptyset_part_emptyset1, emptyparts2 → emptyset_part_emptyset2, emptyparts → emptyset_part_emptyset3; faster proofs
renamed partadequacy → all_partitions_paper_equiv_alg; integrated formerly separate auxiliaries here:
* integrated l14, used more elegant Isar syntax for induction proof
* renamed indstep → all_partitions_paper_equiv_alg_indstep; got rid of mypred (which wasn't elegant due to additional argument x required as a carrier of type 'a)