  In the Boehm theorem workshop on Crete island, Zoran Petric called Statman's
``Typical Ambiguity theorem'' typed Boehm theorem. Moreover, he gave a new
proof of the theorem based on set-theoretical models of the simply typed lambda
calculus. In this paper, we study the linear version of the typed Boehm theorem
on a fragment of Intuitionistic Linear Logic. We show that in the
multiplicative fragment of intuitionistic linear logic without the
multiplicative unit 1 (for short IMLL) weak typed Boehm theorem holds. The
system IMLL exactly corresponds to the linear lambda calculus without
exponentials, additives and logical constants. The system IMLL also exactly
corresponds to the free symmetric monoidal closed category without the unit
object. As far as we know, our separation result is the first one with regard
to these systems in a purely syntactical manner.
