I have a two party protocol, let's call it $M$. At some point, there are $k$ steps, each one involving an oblivious transfer protocol, which is known to be secure against semi honest adversaries. These OT protocoles have independent input and outputs for different steps. Also, I have shown that $M$ is semi-honest if the parties ignore the inside states of each OT protocol. Can I say that $M$ is also secure against semi honest adversaries? Or do I have to include in the view of each adversaries the 'tape' of values involved inside the subroutine OT protocol?
Is it possible to give an answer that does not depend on how OT protocols work. For instance, lets say that a protocol $P$ uses independent instances of $M$ as a subroutine, and suppose $M$ is in fact secure against semi-honest adversaries. Can we say $P$ is secure against semi-honest adversaries?