theorem Th9:
  for L being Ordinal-Sequence,A holds L|Rank A is Ordinal-Sequence
proof
  let L be Ordinal-Sequence, A;
  reconsider K = L|Rank A as Sequence by Th8;
  consider B such that
A1: rng L c= B by ORDINAL2:def 4;
  rng K c= rng L by RELAT_1:70;
  then rng K c= B by A1;
  hence thesis by ORDINAL2:def 4;
end;
