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;
reserve f for non constant standard special_circular_sequence,
  p,p1,p2,p3,q for Point of TOP-REAL 2;

theorem Th11:
  p1 in rng f & p2 in rng f & p3 in rng f & p1..f < p2..f & p2..f
  < p3..f implies p1..Rotate(f,p3) < p2..Rotate(f,p3)
proof
  assume that
A1: p1 in rng f and
A2: p2 in rng f and
A3: p3 in rng f and
A4: p1..f < p2..f & p2..f < p3..f;
  p1..f < p3..f by A4,XXREAL_0:2;
  then
A5: p1..Rotate(f,p3) = len f + p1..f - p3..f by A1,A3,Th9;
  p2..Rotate(f,p3) = len f + p2..f - p3..f & len f + p1..f < len f + p2..f
  by A2,A3,A4,Th9,XREAL_1:6;
  hence thesis by A5,XREAL_1:9;
end;
