reserve D for non empty set,
  f for FinSequence of D,
  g for circular FinSequence of D,
  p,p1,p2,p3,q for Element of D;

theorem Th1:
  q in rng(f|(p..f)) implies q..f <= p..f
proof
  assume
A1: q in rng(f|(p..f));
  then q..(f|(p..f)) = q..f by FINSEQ_5:40;
  then
A2: q..f <= len(f|(p..f)) by A1,FINSEQ_4:21;
  len(f|(p..f)) <= p..f by FINSEQ_5:17;
  hence thesis by A2,XXREAL_0:2;
end;
