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.numbers import Abs, LessEq, Mult, frac, pi, two
from proveit.physics.quantum.QPE import _delta_b_round, _two_pow_t
from proveit.trigonometry import Sin
# build up the expression from sub-expressions
sub_expr1 = Abs(_delta_b_round)
sub_expr2 = Sin(Mult(pi, sub_expr1))
expr = LessEq(frac(Mult(two, _two_pow_t, sub_expr1), sub_expr2), frac(Sin(Mult(_two_pow_t, pi, sub_expr1)), sub_expr2))
# 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()