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Obliq is a lexically-scoped, distributed, object-based programming language. In Obliq, the migration of an object is proposed as creating a clone of the object at the target site, whereafter the original object is turned into an alias for the clone. Obliq has only an informal semantics, so there is no proof that this style of migration is safe i.e., transparent to object clients In previous work, we introduced Ojeblik, an abstraction of~Obliq, where, by lexical scoping sites have been abstracted away. We used Ojeblik in order to exhibit how the semantics behind Obliq's implementation renders migration unsafe. We also suggested a modified semantics that we conjectured instead to be safe. In this paper, we rewrite our modified semantics of \OBLIQ\ in terms of the pi-calculus, and we use it to formally prove the correctness of object surrogation, the abstraction of object migration in Ojeblik