A1: Support p is finite by Def10;
A2: Support q is finite by Def10;
set Sp = Support p;
set Sq = Support q;
(Support p) \/ (Support q) is finite by A1, A2;
then Support (p + q) is finite by Th79, FINSET_1:13;
hence p + q is finite-Support by Def10; :: thesis: verum