theorem Th61:
  for V being non empty CLSStruct, M,N being Subset of V, z being
  Complex st M c= N holds z*M c= z*N
proof
  let V be non empty CLSStruct;
  let M,N be Subset of V;
  let z be Complex;
  assume
A1: M c= N;
  now
    let x be VECTOR of V;
    assume x in z*M;
    then ex w be VECTOR of V st x = z*w & w in M;
    hence x in z*N by A1;
  end;
  hence thesis;
end;
