Debreu-Scarf Theorem (Kreps Proposition 15.11)

以下这个表述和上面的15.11等价吗？还是一个15.11的拓展？

If an allocation for the 1-replica economy, interpreted as an equal-treatment allocation for each N-replica economy, is in the core of each N-replica economy, then for some strictly positive price vector, it is a Walrasian equilibrium allocation for each N-replica economy.