Let R be any ring. The descending chain condition (DCC) for ideals holds in R if every strictly decreasing sequence N₁ ⊃ N₂ ⊃ N₃ ⊃ · · · of ideals in R is of finite length. The minimum condition (mC) for ideals holds in R if given any set S of ideals of R, there is an ideal of S that does not properly contain any other ideal in the set S. Show that for every ring, the conditions DCC and mC are equivalent.