Establish the initial logic/sets/partitions sub-theory package, including the Partitions() and PartitionsMembership() classes. The PartitionsMembership() class is not yet developed.

…embership

Establish the basic axiomatic definition for Partitions(S), some basic theorems defining PartitionsMembership(), and some basic methods for the PartitionsMembership() class. Includes some basic testing in the logic/sets/partitions demmonstrations.ipynb notebook.

Update the basic logic/sets/partitions theorems to correctly use the Disjoint() predicate (in the previous instantiation, I thought I could call Disjoint(P) where P was a set of sets, but instead Disjoint() takes individual set arguments). For convenience in the future it might be useful to have an alternative like DisjointSets(S) that takes a single set of sets as an argument.

Update the logic/sets/partitions/ demonstrations notebook with some efforts to use the Partitions(S) concept in a simple example, mostly failing the demonstration because the partition concept is challenging to use due to the multiple conditions required (non-empty subsets, mutually disjoint, whose union is the original set).

Update the logic/sets/partitions sub-theory package with correction to the use of Disjoint(), changing the condition Disjoint(P) to a Disjoint(A,B) for all A, B in P. Also reorder the conditions in the axiomatic def and related theorems to put the union condition first (per request by WW).

Add a call to self.unfold for PartitionsMembership.side_effcts().

Update the logic/sets/partitions demonstrations.ipynb notebook for recent changes and commits to partitions-related material.

Fix a typo in some comments in the logic/sets/partitions demonstrations.ipynb notebook.

Add one thm to logic/sets/partitions sub-theory pkg: partition_elements_are_subsets. Not yet clear how to incorporate this into a method but seems a reasonably important theorem to have: if x is an element of a partition X, where X is in Partitions(S), then x must be a subset of S.