reserve i,j for Element of NAT,
  x,y,z for FinSequence of COMPLEX,
  c for Element of COMPLEX,
  R,R1,R2 for Element of i-tuples_on COMPLEX;

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;
