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 k, l
from proveit.logic import Forall, Implies
from proveit.numbers import Exp, LessEq, Mult, Sum, frac, one, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _diff_l_scaled_delta_floor, _pos_domain, _two_pow_t
# build up the expression from sub-expressions
sub_expr1 = [l]
expr = Implies(Forall(instance_param_or_params = [k], instance_expr = LessEq(frac(one, Exp(subtract(k, Mult(_two_pow_t, _delta_b_floor)), two)), frac(one, Exp(subtract(k, one), two))), domain = _pos_domain), LessEq(Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(_diff_l_scaled_delta_floor, two)), domain = _pos_domain), Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(subtract(l, one), two)), domain = _pos_domain)))
# 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()