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 B, Conditional, l, m, n
from proveit.core_expr_types import A_1_to_l, C_1_to_m, D_1_to_n
from proveit.logic import And, Boolean, Equals, Forall, InSet
from proveit.numbers import Natural
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [A_1_to_l, B, C_1_to_m, D_1_to_n], instance_expr = Equals(And(A_1_to_l, B, C_1_to_m, D_1_to_n), And(A_1_to_l, C_1_to_m, B, D_1_to_n)).with_wrapping_at(2), domain = Boolean), And(InSet(l, Natural), InSet(m, Natural), InSet(n, Natural)))
# 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()