Let us, for the purposes of this problem only, allow a production of the form

N₁ → rN₂

where N₁ and N₂ are nonterminal and r is a regular expression. The meaning of this formula is that in any working string we may substitute for N1 any string wN₂, where w is a word in the language defined by r. This can be considered a short hand way of writing an infinite family of productions, one for each word in the language of r.
Let a grammar be called bad if all its productions are of the two forms

N₁ → rN₂
N₃ → Λ

Bad grammars generate languages the same way CFGs do.
Prove that even a bad grammar cannot generate a nonregular language, by showing how to construct one regular expression that defines the same language as the whole bad grammar.