theorem Th20:
  L1 is C_Linear_Combination of A & L2 is C_Linear_Combination of
  A implies L1 + L2 is C_Linear_Combination of A
proof
  assume L1 is C_Linear_Combination of A & L2 is C_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 Th19;
  hence Carrier(L1 + L2) c= A by A1;
end;
