theorem Th17:
  dom Seq((g^f)|seq(len g,len f)) = dom f
proof
  rng Sgm(seq(len g,len f)) = seq(len g,len f) by Th12;
  then
A1: rng Sgm(seq(len g,len f)) c= dom (g^f) by Th14;
  dom Seq((g^f)|seq(len g,len f)) = dom (Sgm(seq(len g,len f)) * (g^f))
  by Th16;
  then dom Seq((g^f)|seq(len g,len f)) = dom Sgm(seq(len g,len f))
  by A1,RELAT_1:27;
  hence thesis by Th11;
end;
