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 A, B, Conditional, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, a, b, i, n
from proveit.core_expr_types import a_1_to_n, a_i, b_1_to_n, b_i, v_i
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Interval, one
from proveit.physics.quantum import Bra, Ket, Qmult
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [i]
sub_expr3 = Interval(one, n)
sub_expr4 = Qmult(Ket(v_i), Bra(v_i))
expr = ExprTuple(Lambda([a_1_to_n, b_1_to_n], Conditional(And(Equals(A, VecSum(index_or_indices = sub_expr2, summand = ScalarMult(a_i, sub_expr4), domain = sub_expr3)), Equals(B, VecSum(index_or_indices = sub_expr2, summand = ScalarMult(b_i, sub_expr4), domain = sub_expr3))).with_wrapping_at(2), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, n), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Complex), one, n)))))
# 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()