Induction/Partition of chocolate/Exercise

An ${}n$-chocolate is a rectangular grid, which is divided by ${}a-1$ longitudinal grooves and by ${}b-1$ transverse grooves into ${}n=a\cdot b$ smaller bite-sized rectangles. A dividing step of a chocolate is the complete severing of a chocolate, along a longitudinal or a transverse groove. A complete breakdown of a chocolate is a consequence of division steps (each one applied to a previously obtained intermediate chocolate),

whose final product consists of all the small bite-sized pieces, more handy to be eaten. Show, by induction, that each breakdown of an ${}n$-chocolate consists of exactly ${}n-1$ division steps.

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