
theorem
  for V be non empty addLoopStr, A,B be Subset of V, l be
  C_Linear_Combination of A st A c= B holds l is C_Linear_Combination of B
proof
  let V be non empty addLoopStr;
  let A,B be Subset of V;
  let l be C_Linear_Combination of A;
  assume
A1: A c= B;
  Carrier l c= A by Def4;
  then Carrier l c= B by A1;
  hence thesis by Def4;
end;
