Theorems (or conjectures) for the theory of proveit.logic.sets.functions.images

import proveit
# Prepare this notebook for defining the theorems of a theory:
%theorems_notebook # Keep this at the top following 'import proveit'.

from proveit import f, A, B, S
from proveit.logic import Forall, SubsetEq, Functions, Image

%begin theorems

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

function_image_is_within_codomain = Forall(
    (A, B, S), Forall(
        f, SubsetEq(Image(f, S), B),
        domain=Functions(A, B)),
    condition=SubsetEq(S, A))

function_image_is_within_codomain (conjecture without proof):

%end theorems

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