theorem Th44:
  (r(#)seq)"=r"(#)seq"
proof
  now
    let n be Element of NAT;
    thus (r(#)seq)".n=((r(#)seq).n)" by VALUED_1:10
      .=(r*(seq.n))" by Th9
      .=r"*(seq.n)" by XCMPLX_1:204
      .=r"*seq".n by VALUED_1:10
      .=(r"(#)seq").n by Th9;
  end;
  hence thesis by FUNCT_2:63;
end;
