"Ignoring the more technical definition, Rubin (1996) states the following main
conditions. The multiple imputations are said to be proper if:
1. MI estimates bQMI are asymptotically normal with mean bQ and a consistent variance–covariance estimate B.
2. The within-imputation variance estimateW is a consistent estimate of the variance–covariance estimate U with variability of a lower order than Var(bQMI)."
-Stata Help Manual
Oh yes!!! That's right! I forgot that Rubin ignored the more technical definition. Silly me!