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 l
from proveit.logic import Forall, Implies, InSet
from proveit.numbers import Exp, Real, Sum, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain
# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = frac(one, Exp(_diff_l_scaled_delta_floor, two))
expr = Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(sub_expr2, Real), domain = _neg_domain), InSet(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = _neg_domain), Real))
# 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()