theorem Th24:
  L1 is Linear_Combination of A & L2 is Linear_Combination of A
  implies L1 + L2 is Linear_Combination of A
proof
  assume L1 is Linear_Combination of A & L2 is Linear_Combination of A;
  then Carrier(L1) c= A & Carrier(L2) c= A by Def4;
  then
A1: Carrier(L1) \/ Carrier(L2) c= A by XBOOLE_1:8;
  Carrier(L1 + L2) c= Carrier(L1) \/ Carrier(L2) by Th23;
  hence Carrier(L1 + L2) c= A by A1;
end;
