Let N be a transitive model of ZFC such that “N ⊂ N and P(ℝ) ⊂ N. Assume that both V and N satisfy “the core model K exists.” Then KN is an iterate of K, i.e., there exists an iteration tree F on K such that F has successor length and . Moreover, if there exists an elementary embedding π: V → N then the iteration map associated to the main branch of F equals π յ K. (This answers a question of W. H. Woodin, M. Gitik, and others.) The hypothesis that P(ℝ) ⊂ N is not needed if there does not exist a transitive model of ZFC with infinitely many Woodin cardinals.