theorem Th8:
  for L being Sequence,A holds L|Rank A is Sequence
proof
  let L be Sequence, A;
A1: dom(L|Rank A) = dom L /\ Rank A by RELAT_1:61;
  now
    let X;
    assume
A2: X in dom(L|Rank A);
    then
A3: X in dom L by A1,XBOOLE_0:def 4;
    hence X is Ordinal;
    X in Rank A by A1,A2,XBOOLE_0:def 4;
    then
A4: X c= Rank A by ORDINAL1:def 2;
    X c= dom L by A3,ORDINAL1:def 2;
    hence X c= dom(L|Rank A) by A1,A4,XBOOLE_1:19;
  end;
  then dom(L|Rank A) is epsilon-transitive epsilon-connected set
by ORDINAL1:19;
  hence thesis by ORDINAL1:31;
end;
