Axioms for the theory of proveit.logic.sets.power_set

import proveit
# Prepare this notebook for defining the axioms of a theory:
%axioms_notebook # Keep this at the top following 'import proveit'.
from proveit import x, S
from proveit.logic import Equals, Forall, InSet, PowerSet, SubsetEq

%begin axioms

Defining axioms for theory 'proveit.logic.sets.power_set'
Subsequent end-of-cell assignments will define axioms
%end_axioms will finalize the definitions

power_set_def = Forall((x, S), Equals(InSet(x, PowerSet(S)),
                                      SubsetEq(x, S)))

power_set_def:

%end axioms

These axioms may now be imported from the theory package: proveit.logic.sets.power_set