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 Th4:
  p in rng f & q in rng f & p..f <= q..f implies q..Rotate(f,p) = q
  ..f - p..f + 1
proof
  assume that
A1: p in rng f and
A2: q in rng f;
A3: Rotate(f,p) = (f:-p)^((f-:p)/^1) by A1,FINSEQ_6:def 2;
  assume
A4: p..f <= q..f;
  then q in rng(f:-p) by A1,A2,FINSEQ_6:62;
  hence q..Rotate(f,p) = q..(f:-p) by A3,FINSEQ_6:6
    .= q..f - p..f + 1 by A1,A2,A4,Th2;
end;
