  Kim's Lemma is a key ingredient in the theory of forking independence in
simple theories. It asserts that if a formula divides, then it divides along
every Morley sequence in type of the parameters. Variants of Kim's Lemma have
formed the core of the theories of independence in two orthogonal
generalizations of simplicity - namely, the classes of NTP2 and NSOP1 theories.
We introduce a new variant of Kim's Lemma that simultaneously generalizes the
NTP2 and NSOP1 variants. We explore examples and non-examples in which this
lemma holds, discuss implications with syntactic properties of theories, and
ask several questions.
