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 Th7:
  p in rng g & len g > 1 implies p..g < len g
proof
  assume that
A1: p in rng g and
A2: len g > 1 and
A3: p..g >= len g;
  p..g <= len g by A1,FINSEQ_4:21;
  then p..g = len g by A3,XXREAL_0:1;
  then
A4: p = g/.len g by A1,FINSEQ_5:38
    .= g/.1 by FINSEQ_6:def 1;
  g is non empty by A2,CARD_1:27;
  hence contradiction by A2,A3,A4,FINSEQ_6:43;
end;
