Let Σ be a (non-empty) alphabet and let w ∈ Σ∗ be a string. We say that x ∈ Σ∗ is a prefix of the string w if there exists a string u ∈ Σ∗ such that w = xu. Consider the following language: L = {w ∈ {a, b}∗: for every prefix x of w nb(x) ≥ na(x)} Prove that L is a context-free language. Your proof should rely on mathematical induction.

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