Let EVEN-CFL $=\left\{w | M_{w} \text { is a } \mathrm{TM}, \text { such that } L\left(M_{w} \right) \\ \text{ has only words with even length and is context free.}\right .\}$
Question : Is EVEN-CFL decidable?
Am trying to learn this type of proofs
Now the Rice-Theorem states, that semantic properties that are non-trivial are undecidable.
For this, EVEN-CFL is not a syntactic property of a TM, it's a property of the language and it's non-trivial because there exists languages that are context free and others that are not, like recursive languages or they have the length or not.
Is this right so far? How do I proceed now is this it? The use of the RICE-THEOREM
Thanks