In Adamek and Rosickys' Locally Presentable and Accessible Categories, I came across the following statement (I'm paraphrasing),
every $\mu$-presentable object in a locally $\lambda$-presentable category (for regular cardinals $\mu\geq\lambda$) is a $\mu$-small colimit of $\lambda$- presentable objects. The proof is rather technical, however the following weaker statement is trivial: each $\mu$-presentable object is a split quotient of a $\mu$-small colimit of $\lambda$-presentable objects.
The book then goes on to prove the second statement. But, doesn't this statement directly prove the first as a split quotient can be expressed as a coequaliser between the corresponding split idempotent and the identity map, making it a coequaliser of a $\mu$-small colimit of $\lambda$-presentable objects and hence a $\mu$-small colimit of $\lambda$-presentable objects itself?