theorem
  for V being ComplexLinearSpace, L being C_Linear_Combination of V st L
  is convex holds L <> ZeroCLC V
proof
  let V be ComplexLinearSpace;
  let L be C_Linear_Combination of V;
  assume L is convex;
  then
A1: Carrier L <> {} by Th77;
  assume L = ZeroCLC V;
  hence contradiction by A1;
end;
