theorem Th11:
  for a being Complex holds dom(a*x) = dom x
proof
  let a be Complex;
  dom(a multcomplex) = COMPLEX by FUNCT_2:def 1;
  then rng x c= dom(a multcomplex) by FINSEQ_1:def 4;
  hence dom x = dom((a multcomplex)*x) by RELAT_1:27
    .= dom(a*x) by SEQ_4:def 9;
end;
