The cylindrical parts of a system of real algebraic equations and inequalities in variables {x_1, ..., x_n} are the terms f_1 | <= | x_1<=g_1 f_2(x_1) | <= | x_2<=g_2(x_1) | ⋮ | f_n(x_1, x_2, ..., x_n) | <= | x_n<=g_n(x_1, ..., x_(n - 1)), where '<=' is one of <, <=, or = , and f_i and g_i are ± ∞ or algebraic expressions in variables {x_1, ..., x_(i - 1)} that are real-valued for all (i - 1)-tuples of real numbers {a_1, ..., a_(i - 1)} satisfying