Bach's 6 Little Preludes vs Inventions and Sinfonias

[janvan]

I have recently started to learn the 6 little preludes (BWV 933-938) and noticed that they follow the same key scheme as the first 6 inventions and sinfonias.

Could it be that Bach composed a full set of 15 little preludes (of which some may be lost) to complement the inventions and sinfonias?

I somehow get the impression that the little preludes prepare for the preludes of the WTC in the same way as the inventions and sinfonias prepare for the fugues of the WTC.

I'm wondering, are the little preludes really that much easier than the 2-part inventions or are they just as difficult but in a different way? And, how do they fit into the larger context of Bach's pedagogical keyboard pieces?