reserve i,j,k,n for Nat;

theorem Th11:
  for f being clockwise_oriented non constant standard
special_circular_sequence for p being Point of TOP-REAL 2 st p`2 < S-bound (L~f
  ) holds p in LeftComp f
proof
  let f be clockwise_oriented non constant standard special_circular_sequence;
  let p be Point of TOP-REAL 2;
  set g = Rotate(f,N-min L~f);
A1: L~f = L~g by REVROT_1:33;
  assume
A2: p`2 < S-bound (L~f);
  N-min L~f in rng f by SPRECT_2:39;
  then g/.1 = N-min L~g by A1,FINSEQ_6:92;
  then p in LeftComp g by A1,A2,JORDAN2C:112;
  hence thesis by REVROT_1:36;
end;
