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 Conditional, ExprTuple, Lambda, gamma, i, y
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Interval, Mult, four, two
# build up the expression from sub-expressions
sub_expr1 = Interval(two, four)
sub_expr2 = ScalarMult(ScalarMult(gamma, i), y)
sub_expr3 = ScalarMult(Mult(gamma, i), y)
sub_expr4 = InSet(i, sub_expr1)
expr = ExprTuple(Forall(instance_param_or_params = [i], instance_expr = Equals(sub_expr2, sub_expr3), domain = sub_expr1), Equals(Lambda(i, Conditional(sub_expr2, sub_expr4)), Lambda(i, Conditional(sub_expr3, sub_expr4))).with_wrapping_at(2))
# 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()