
theorem Th20:
  for n being set, L being right_zeroed non empty addLoopStr, p,
  q being Series of n, L holds Support (p+q) c= Support p \/ Support q
proof
  let n be set, L be right_zeroed non empty addLoopStr, p, q be Series of n,
  L;
  set f = p+q, Sp = Support p, Sq = Support q;
  let x be object;
  assume
A1: x in Support f;
  then reconsider x9 = x as Element of Bags n;
  f.x9 <> 0.L by A1,Def4;
  then p.x9+q.x9 <> 0.L by Th15;
  then not(p.x9 = 0.L & q.x9 = 0.L) by RLVECT_1:def 4;
  then x9 in Sp or x9 in Sq by Def4;
  hence thesis by XBOOLE_0:def 3;
end;
