The set $\Lambda$ is given inductively by:
- $x\in\Lambda$, if $x$ is a variable;
- $(\lambda x M)$, if $x$ is a variable and $M\in\Lambda$;
- $(MN)$, if both $M,N\in\Lambda$.
Now, consider the structural induction principle associated with $\Lambda$. Say a property $P(M)$ over $M\in\Lambda$. Consider just the second case; is it(?)
- $P(x)\wedge P(M)\implies P(\lambda x M)$, for all $x$ variable and $M\in\Lambda$.