Lemma 8.5

Lemma 8.5 (Mirror-prefix lemma). Let $Y$ be a nonempty even palindrome and $c$ a letter.

1. If $D_c(Y)$ is defined, the final palindrome of $\Pi(cD_c(Y)c,\omega_c(Y))$ is $F=Yc\,\omega_c(Y)$, and $\lambda(F)=Y$.

2. If $D_c(Y)$ is undefined, the final palindrome of $\Pi(\epsilon,cY)$ is $F=YccY$, and $\lambda(F)=Y$.

In both cases the last receipt of the rope is the anchor’s source $Y$ itself.