We define an $i$ - access PDA as a PDA that can manipulate the top $i$ characters in the stack, where $i>0$.
Given a transition function of the form $\delta(p,x,c,d) \to (q,c')$, where $d \le i, d > 0$, we read it as "When in state $p$, upon reading an input $x$, the stack has depth at least $d$, with $c$ at the $d$th position from the top. Transition to $q$, pop $c$, and add $c'$ at the same index as $c$.
In essence, a $1$ - access PDA is essentially a normal PDA.
How do I show that for any language accepted by an $i$ - access PDA, $\exists$ a normal PDA which accepts it as well?
I know that I have to show that in the end, any $i$ - access PDAs can be reduced down to a $1$ - access PDA. But I am not sure how to go about it.