How i can use Mathematical induction to prove CFG production?

Question

If I have production $G_n$

$S \rightarrow A_i b_i \quad$ for $1 \le i \le n$

$A_i \rightarrow a_j A_i \mid a_j\quad$ for $1 \le i$ and $i \ne j$

1. Prove $G_n$ is sub-productions from $2n^2 - n$
2. Prove $G_n$ is $LR(0)$ production from $2^n + n^2 + n$