bounded PDA and context-free languages

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How can we prove that:

Class of linear bounded PDA languages ∼ Class of CFLs

I know that for a linear bounded PDA there is a constant k such that the stack size for w is at most k|w|. I also read about PDA's and CFL's and know that pushdown automata are essentially finite automata with a stack as storage and a grammar G = (V, T, S, P) is said to be context-free if all productions in P have the form A → x

How can this be used to show that they are equivalent?

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