**Original manuscript:** 1998/05/19
**Manuscript last revised:** 2001/08/17

We provide two natural ways to lift a distribution from a manifold to its
tangent bundle, and show that they agree if and only if the original
distribution is integrable. The case when the manifold is the total space of
a fibration over **R** is particularly interesting as the two
constructions interact with the affine structure of the jet bundles in the
``same'' way.

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Last Updated: Fri Jul 10 09:36:20 2020