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Context: proveit.logic.set_theory

Basic set theory context dealing with membership (e.g., $x \in S$), enumeration (e.g., $\{e_1, e_2, e_3\}$), containment (e.g., $A \subseteq B$), unification (e.g., $A \cup B \cup C$), intersection (e.g., $A \cap B \cap C$), subtraction (e.g., $A - B$), comprehension (e.g., $\{f(x)~|~Q(x)\}_{x \in S}$), and cardinatly (e.g., $|S|$).

In [1]:
import proveit
%context
common expressions axioms theorems demonstrations
membershipIs an element a member of a set? Not a member of a set?
enumerationDefine a set by enumerating its contents.
containmentIs one set contained by another?
unificationDefine a set as the union of sets.
intersectionDefine a set as the intersection of sets.
subtractionDefine a set by removing elements from an original set.
comprehensionDefine a set according to the properties of its members.
disjointnessAre their common elements between sets? Also defines "distinct".
cardinalityHow large is a set?