renamed allpartitionsoflist → all_partitions_of_list
renamed l5 → subset_is_partition, and simplified
one definition for "all partitions of a set" is sufficient:
* kept allpartitions → all_partitions
* removed allpartitionsofset
renamed l6 → partition_extension, simplified
renamed l7 → disj_eq_classes, slightly cleaned up
renamed l4 → partition_extension2, made more readable
renamed partition_extension → partition_extension1
renamed l1 → partition_extension3 and gave it an easier structure
renamed l10 → image_union, l11 → no_empty_eq_class, started making l2a more readable