# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(t, one)
sub_expr3 = Add(t, _s)
sub_expr4 = Interval(sub_expr2, sub_expr3)
sub_expr5 = Interval(one, sub_expr3)
sub_expr6 = MultiQubitElem(element = Gate(operation = QPE1(_U, t), part = sub_expr1), targets = sub_expr5)
sub_expr7 = MultiQubitElem(element = Output(state = TensorProd(_psi_t_ket, _ket_u), part = sub_expr1), targets = sub_expr5)
sub_expr8 = [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _psi_t_ket, part = sub_expr1), targets = Interval(one, t)), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr4), one, _s)]
sub_expr9 = [ExprRange(sub_expr1, Input(state = ket_plus), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr4), one, _s)]
sub_expr10 = [ExprRange(sub_expr1, sub_expr6, one, t), ExprRange(sub_expr1, sub_expr6, sub_expr2, sub_expr3)]
sub_expr11 = [ExprRange(sub_expr1, sub_expr7, one, t).with_wrapping_at(2,6), ExprRange(sub_expr1, sub_expr7, sub_expr2, sub_expr3).with_wrapping_at(2,6)]
expr = Implies(QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray(sub_expr8)), Qcircuit(vert_expr_array = VertExprArray(sub_expr11))), QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray(sub_expr9, sub_expr10, sub_expr8)), Qcircuit(vert_expr_array = VertExprArray(sub_expr9, sub_expr10, sub_expr11))).with_wrapping_at(1)).with_wrapping_at(2)