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 Conditional, Lambda, k, t
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals, Forall, Implies, InSet
from proveit.numbers import Add, Interval, one, subtract, zero
from proveit.physics.quantum import NumKet, ket0
from proveit.physics.quantum.QPE import two_pow_t
# build up the expression from sub-expressions
sub_expr1 = NumKet(k, Add(t, one))
sub_expr2 = TensorProd(ket0, NumKet(k, t))
sub_expr3 = Interval(zero, subtract(two_pow_t, one))
sub_expr4 = InSet(k, sub_expr3)
expr = Implies(Forall(instance_param_or_params = [k], instance_expr = Equals(sub_expr1, sub_expr2), domain = sub_expr3), Equals(Lambda(k, Conditional(sub_expr1, sub_expr4)), Lambda(k, Conditional(sub_expr2, sub_expr4))).with_wrapping_at(2)).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()