  We show that any smooth and proper dg-algebra (over some base ring k) is
determined, up to quasi-isomorphism, by its underlying A_n-algebra, for a
certain integer n. Similarly, any morphism between two smooth and proper
dg-algebras is determined, up to homotopy, by the morphism induced on the
underlying A_n-algebras, for a certain integer n. When the base ring k is
local, we show that the integer n can be chosen uniformally for all smooth and
proper dg-algebras for which two numerical invariants (the "type" and the
"cohomogical dimension") are bounded.
