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 ExprRange, Lambda, Variable, t
from proveit.core_expr_types import Len
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals
from proveit.numbers import Add, Interval, one, two
from proveit.physics.quantum.QPE import _ket_u, _psi_t_ket, _s
from proveit.physics.quantum.circuits import MultiQubitElem, Output
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = TensorProd(_psi_t_ket, _ket_u)
sub_expr3 = Interval(one, Add(t, _s))
expr = Equals(Len(operands = [Lambda(Variable("_b", latex_format = r"{_{-}b}"), MultiQubitElem(element = Output(state = sub_expr2, part = one), targets = sub_expr3)), Lambda(sub_expr1, MultiQubitElem(element = Output(state = sub_expr2, part = Add(sub_expr1, t)), targets = sub_expr3))]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, two)]))
# 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()