  Let T be an NIP L-theory and T' be an enrichment. We give a sufficient
condition on T' for the underlying L-type of any definable (respectively
invariant) type over a model of T' to be definable (respectively invariant) as
an L-type. Besides, we generalise work of Simon and Starchenko on the density
of definable types among non forking types to this relative setting. These
results are then applied to Scanlon's model completion of valued differential
fields.
