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, a_star, b, b_star
from proveit.logic import And, Equals, Exists, FALSE, Forall, Implies
from proveit.numbers import Abs, GCD, NaturalPos, frac, one, sqrt, two
# build up the expression from sub-expressions
sub_expr1 = Abs(sqrt(two))
expr = Implies(And(Exists(instance_param_or_params = [a, b], instance_expr = And(Equals(sub_expr1, frac(a, b)), Equals(GCD(a, b), one)), domain = NaturalPos), Forall(instance_param_or_params = [a_star, b_star], instance_expr = Implies(And(Equals(sub_expr1, frac(a_star, b_star)), Equals(GCD(a_star, b_star), one)), FALSE), domain = NaturalPos)), FALSE)
# 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()