Axioms for the theory of proveit.logic.sets.functions.images

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 f, x, fx, A
from proveit.logic import Forall, Equals, SetOfAll, Image

%begin axioms

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

The image of a set under a function is the set obtained by applying the function to each element of that original set.

set_image_def = Forall(
    (f, A), Equals(Image(f, A), 
                   SetOfAll(x, fx, domain=A)))

set_image_def:

%end axioms

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