Using the security definition in the malicious model to prove security in the semi honest model Can I use the security definition in the malicious model in order to prove the security of a two-party protocol which is in the semi-honest model? (I am using IDEAL/REAL Model paradigm)

Would you please explain it to me?

These definitions are from "Efficient Secure Two-Party Protocols-Hazay-Lindell"
Definition 2.3.1 (Malicious model)



Definition 2.2.1 (Semi honest model)



-
No, you cannot do this, because, as explained further in the book, security against malicious adversaries does not imply security against semi-honest ones.