let X be set ; :: thesis: support (EmptyBag X) = {}
assume support (EmptyBag X) <> {} ; :: thesis: contradiction
then reconsider S = support (EmptyBag X) as non empty set ;
consider u being Element of S;
(EmptyBag X) . u <> 0 by POLYNOM1:def 7;
hence contradiction by POLYNOM1:56; :: thesis: verum