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
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.logic import CartExp, Forall, Implies, InSet
from proveit.numbers import Complex, Exp, Mult, e, i, pi, two
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.QPE import _m_domain, _phase, _t, _two_pow_t
# build up the expression from sub-expressions
sub_expr1 = [k]
sub_expr2 = CartExp(Complex, _two_pow_t)
sub_expr3 = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, _t))
expr = Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(sub_expr3, sub_expr2), domain = _m_domain), InSet(VecSum(index_or_indices = sub_expr1, summand = sub_expr3, domain = _m_domain), sub_expr2)).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()