import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import a, b, f, i, j, k, l
from proveit.core_expr_types.tuples import shift_equiv_both
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, Integer, Natural, one, subtract
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [f], instance_expr = Forall(instance_param_or_params = [a, b], instance_expr = Forall(instance_param_or_params = [i, j, k, l], instance_expr = shift_equiv_both, conditions = [InSet(subtract(Add(j, one), i), Natural), Equals(Add(i, a), Add(k, b)), Equals(Add(j, a), Add(l, b))]), domain = Integer))
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
stored_expr.style_options()
# display the expression information
stored_expr.expr_info()